You may try R-Studio for free. R-Studio Demo does everything except it does not save recovered files larger than 256 KB.
With R-Studio Demo you may search for the lost files, scan disks, create virtual RAIDs, etc. When you've found your lost files you may estimate chances for recovery by previewing the files. If the files are previewed successfully, you may buy R-Studio and register it on-the-fly, and no re-installation is required. Then you can recover the lost files found.
If you just format the disk, this article will help:Data Recovery from a Re-Formatted exFAT Disk
. The article describes recovery from another files system than you, but general guidelines are the same. You'll be able to recover some files with full file names and paths, some with their content only. The proportion cannot be determined until the recovery.
If you re-installed the system, this article will help: File Recovery after Re-installing Windows