Ouch! It's odd that the mistakenly formatted drive won't show on the desktop. An exFAT drive should still be visible.
This won't be easy. Typical Windows recovery software depends on the file table to determine what files are on the drive and where to recover them from. Formatting the drive wiped out the file table. But this was a Mac formatted partition to begin with.
You can give FileSalvage a try. It will run as a working demo and allow you to recover a few files to see if it works. I recommend this one in particular because it has an option called Salvage All Files, which will attempt to recover data from a drive that won't mount on the desktop.
This is a very long process, especially on such a large drive/partition. It works by examining the entire drive for BOF (beginning of file) markers, and then recovering whatever it can.
Do not write anything to the drive you need to recover data from. If you know there's more data on the ABC drive to recover than will fit on the 250 GB partition, then you'll need an external drive large enough to hold the recovered data. You can't save it back to the same drive you're recovering data from. One, the software won't let you. And two, that's because writing recovered data to the drive could destroy other data that hasn't been recovered yet.