Revenue Recognition - Other Revenue (Details) - USD ($) $ in Thousands	3 Months Ended	9 Months Ended
Sep. 30, 2021	Sep. 30, 2020	Sep. 30, 2021	Sep. 30, 2020
Revenue from Contract with Customer [Abstract]
Revenue gross-up	$ 201,704	$ 97,566	$ 526,082	$ 315,049

Revenue from Contract with Customer, Excluding Assessed Tax, Gross

No definition available.

Name:	ae_RevenueFromContractWithCustomerExcludingAssessedTaxGross
Namespace Prefix:	ae_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration