I have a machine with ArcGIS for Desktop 10.0 installed on it.
I need to find out which license it's using.
The machine is single use ArcEditor and was authorized online.
How can I find what the license number is?
go to customers.esri.com and log in as the administrator for your company.
Go to the ArcGIS Administrator located on the Start Menu > All Programs > ArcGIS > ArcGIS Administrator. From there look at the "License Manager Environment Variable Information" section under "ARCGIS_LICENSE_FILE:xxxxxx". Also look at the "Machine IDs..." tab on the main layout.
Edit (Additional information from @Brad):