Take a look at the Oracle website on Minimum technical requirements -
https://support.oracle.com/CSP/ui/flash.html#tab=KBHome(page=KBHome&id=()),(page=KBNavigator&id=(viewingMode=1143&bmDocTitle=JD%20Edwards%20EnterpriseOne%20Current%20MTR%20Index&bmDocID=747323.1&bmDocType=REFERENCE&from=BOOKMARK&bmDocDsrc=KB))
Here is what it says you can use for a terminal server:
"Note: Windows Server 2008 is only supported as 64 bit. Itanium is not supported.
Note: Windows 2008 x64 (64 bit) SP1 is supported beginning with JD Edwards EnterpriseOne Tools SP24.0.0.
Note: Windows 2008 x64 (64 bit) SP2 is supported beginning with JD Edwards EnterpriseOne Tools SP24.0.0.
Note: To use Windows 2008 x64 (64 bit) as a Windows Terminal Server you must switch from remote administration to application mode.
Note: EnterpriseOne runs as a 32 bit application on Windows Server 2008 x64 (64 bit)
Note: To install EnterpriseOne on a Windows Server 2008 x64 (64 bit) Terminal Server the user must use ‘run as administrator’. Users running E1 on Windows Server 2008 x64 (64 bit) Terminal Server do not need to be administrators.
Note: Oracle validates JD Edwards EnterpriseOne products with Microsoft Windows Server 2008 x64 (64 bit) Standard Edition. This validation also extends to Windows Server 2008 x64 (64 bit) Enterprise Edition and x64 (64 bit) Datacenter Edition. Customers who choose to implement EnterpriseOne on Windows Server 2008 x64 964 bit) Enterprise Edition or x64 964 bit) Datacenter Edition will receive support services according to their EnterpriseOne services agreement. Hyper-V and Server Core versions are not supported.
Note: When installing or running E1 components on Windows Server 2008 the user must use ‘run as administrator’. This can be accomplished by right-clicking the executable and selecting ‘Run As Administrator’ from the drop-down menu."
Linux is not an option for an XE terminal server replacement.