It looks like you own both PRS-350 and PRS-T2.
Just a reminder that Adobe Digital Edition software no longer works with PRS-T1/T2/T3.
If you wish to manage eBooks with both devices, then I would suggest to use the latest 'Reader for PC/Mac' app.
Others prefer to use Calibre, but I personally stay away to avoid any risk with a non-official app that could screw my devices up. If I have issues with 'Reader for PC', I simply report to Sony's customer support for future improvements. Fortunately, I do not have any major issue with the Sony's app. I understand, however, everyone has different preferences.