Text Edit rtf. Document suddenly disappeared from desktop after opening it!
Local Time Machine snapshot
If you enabled Time Machine and didn't disable local snapshots in the past (but can't back up your files at the moment because the backup volume is at home/elsewhere) you should be able to find the file in the local Time Machine snapshot.

Open Time Machine
In the &quot;Star Wars&quot; display navigate to your desktop folder
White/purple ticks at the right side indicate local snapshots/snapshots on the Time Machine backup volume
Use the white ticks to search for your lost document

Containers
A second place to find the file - independent of any backups - may be:
/Users/your_user_name/Library/Containers/com.apple.TextEdit/Data/Library/Autosave Information/