There are a lot of tools out there that allow you to recover data from a hard drive that was either deleted by accident, or overwritten. Of course these tools are rarely 100% effective, depending on the age of the drive, and the number of passes of data that have overwritten the target data. Based on your description of the issue, it sounds like it essentially formatted your drive, and then wrote over it once, with the new OS. If that is the case, it's actually fairly easy to obtain that data again. Some tools that are available include EaseUS and Recuva. I've used the paid version EaseUS in the past to recover pictures on a drive that had been reformatted by Windows attempting to do a system recovery, and was able to succesfully pull about 90% of the pictures off of it. A lot of these offer "free" versions but usually limit the amount of data that can be recovered. You can look over this LifeWire article on free software as well and take your pick.
Good luck! Perhaps next time you'll read a little more carefully before formatting a drive. ;)
photorec
and runsudo photorec
, select the disk to scan, the filetypes in this case images (png, jpeg, jpg,raw,gif), and the target where to save the findings which should be a different disk like a usb disk/stick. The only issue is that found files don't have the original name. – bistoco Apr 05 '17 at 17:08