Related Party Transactions - Additional Information (Details) - USD ($) $ / shares in Units, $ in Millions	Feb. 13, 2024	Apr. 04, 2023
April 2023 Notes
Related Party Transaction [Line Items]
Principal amount		$ 8.0
Interest free period		45 days
Interest rate		15.00%
Amount of convertible debentures and warrants		$ 8.0
Maturity date		Jul. 31, 2023
Minimum \| April 2023 Notes
Related Party Transaction [Line Items]
Aggregate sale of convertible promissory notes, warrants, preferred shares, common shares, or combined thereof		$ 20.0
2024 Subscription Agreements \| Private Placement
Related Party Transaction [Line Items]
Issuance of common shares	20,000,000
Common shares price per share	$ 10
2024 PIPE Investors
Related Party Transaction [Line Items]
Issuance of common shares	800,000
Issuance of common shares, value	$ 8.0

Aggregate sale of convertible promissory notes warrants preferred shares common shares or combined thereof.

No definition available.

Name:	engn_AggregateSaleOfConvertiblePromissoryNotesWarrantsPreferredSharesCommonSharesOrCombinedThereof
Namespace Prefix:	engn_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Convertible debentures and warrants.

+ References

No definition available.

+ Details

Name:	engn_ConvertibleDebenturesAndWarrants
Namespace Prefix:	engn_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- Definition

Debt instrument interest free period.

+ References

No definition available.

+ Details

Name:	engn_DebtInstrumentInterestFreePeriod
Namespace Prefix:	engn_
Data Type:	xbrli:durationItemType
Balance Type:	na
Period Type:	instant

- Definition

Face amount or stated value per share of common stock.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Topic 210
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(29))
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147480566/210-10-S99-1

+ Details

Name:	us-gaap_CommonStockParOrStatedValuePerShare
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:perShareItemType
Balance Type:	na
Period Type:	instant

- Definition

Face (par) amount of debt instrument at time of issuance.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 835
-SubTopic 30
-Name Accounting Standards Codification
-Section 50
-Paragraph 1
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147482900/835-30-50-1

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 470
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 1B
-Subparagraph (a)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147481139/470-20-50-1B

Reference 3: http://www.xbrl.org/2003/role/exampleRef
-Topic 470
-SubTopic 20
-Name Accounting Standards Codification
-Section 55
-Paragraph 69B
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147481568/470-20-55-69B

Reference 4: http://www.xbrl.org/2003/role/exampleRef
-Topic 470
-SubTopic 20
-Name Accounting Standards Codification
-Section 55
-Paragraph 69C
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147481568/470-20-55-69C

Reference 5: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Topic 835
-SubTopic 30
-Section 45
-Paragraph 2
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147482925/835-30-45-2

Reference 6: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Topic 835
-SubTopic 30
-Section 55
-Paragraph 8
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147482949/835-30-55-8

+ Details

Name:	us-gaap_DebtInstrumentFaceAmount
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Date when the debt instrument is scheduled to be fully repaid, in YYYY-MM-DD format.

+ References

Reference 1: http://www.xbrl.org/2003/role/exampleRef
-Topic 470
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 1B
-Subparagraph (d)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147481139/470-20-50-1B

Reference 2: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 820
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (bbb)(2)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147482106/820-10-50-2

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02.22(a)(2))
-SubTopic 10
-Topic 210
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147480566/210-10-S99-1

+ Details

Name:	us-gaap_DebtInstrumentMaturityDate
Namespace Prefix:	us-gaap_
Data Type:	xbrli:dateItemType
Balance Type:	na
Period Type:	duration

- Definition

Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 946
-SubTopic 220
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.6-07(2)(c)(2)(i))
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147483575/946-220-S99-1

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 946
-SubTopic 220
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.6-07(2)(c)(2)(ii))
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147483575/946-220-S99-1

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Topic 946
-SubTopic 220
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.6-07(2)(g)(3))
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147483575/946-220-S99-1

+ Details

Name:	us-gaap_RelatedPartyTransactionLineItems
Namespace Prefix:	us-gaap_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Definition

Identify the stated interest rate per the agreement, for example, leasing and debt arrangements between related parties.

+ References

No definition available.

+ Details

Name:	us-gaap_RelatedPartyTransactionRate
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	duration

- Definition

Number of new stock issued during the period.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-SubTopic 10
-Topic 505
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147481112/505-10-50-2

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 946
-SubTopic 505
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (a)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147481004/946-505-50-2

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Topic 946
-SubTopic 220
-Name Accounting Standards Codification
-Section S99
-Paragraph 3
-Subparagraph (SX 210.6-09(4)(b))
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147483575/946-220-S99-3

Reference 4: http://www.xbrl.org/2003/role/disclosureRef
-Topic 946
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 3
-Subparagraph (SX 210.6-03(i)(1))
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147479886/946-10-S99-3

Reference 5: http://fasb.org/us-gaap/role/ref/legacyRef
-Topic 210
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(28))
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147480566/210-10-S99-1

Reference 6: http://fasb.org/us-gaap/role/ref/legacyRef
-Topic 505
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.3-04)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147480008/505-10-S99-1

Reference 7: http://fasb.org/us-gaap/role/ref/legacyRef
-Topic 210
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(29))
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147480566/210-10-S99-1

+ Details

Name:	us-gaap_StockIssuedDuringPeriodSharesNewIssues
Namespace Prefix:	us-gaap_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	duration

- Definition

Equity impact of the value of new stock issued during the period. Includes shares issued in an initial public offering or a secondary public offering.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-SubTopic 10
-Topic 505
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147481112/505-10-50-2

Reference 2: http://www.xbrl.org/2003/role/exampleRef
-Topic 946
-SubTopic 830
-Name Accounting Standards Codification
-Section 55
-Paragraph 11
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147480167/946-830-55-11

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Topic 946
-SubTopic 205
-Name Accounting Standards Codification
-Section 45
-Paragraph 4
-Subparagraph (a)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147480767/946-205-45-4

Reference 4: http://www.xbrl.org/2003/role/disclosureRef
-Topic 946
-SubTopic 505
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (a)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147481004/946-505-50-2

Reference 5: http://www.xbrl.org/2003/role/disclosureRef
-Topic 946
-SubTopic 220
-Name Accounting Standards Codification
-Section S99
-Paragraph 3
-Subparagraph (SX 210.6-09(4)(b))
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147483575/946-220-S99-3

Reference 6: http://fasb.org/us-gaap/role/ref/legacyRef
-Topic 210
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(28))
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147480566/210-10-S99-1

Reference 7: http://fasb.org/us-gaap/role/ref/legacyRef
-Topic 505
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.3-04)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147480008/505-10-S99-1

Reference 8: http://fasb.org/us-gaap/role/ref/legacyRef
-Topic 210
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(29))
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147480566/210-10-S99-1

+ Details

Name:	us-gaap_StockIssuedDuringPeriodValueNewIssues
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- Details

Name:	us-gaap_DebtInstrumentAxis=engn_AprilTwentyTwentyThreeNotesMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	srt_RangeAxis=srt_MinimumMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_TypeOfArrangementAxis=engn_SubscriptionAgreementsMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_SubsidiarySaleOfStockAxis=us-gaap_PrivatePlacementMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_TypeOfArrangementAxis=engn_TwoThousandTwentyFourPipeInvestorsMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: