If affordable and possible, clone this entire HD, as is, onto an external HD. After giving that ext HD a unique name, store that "copy" in a safe place, you might need that for future data recovery attempts. Meanwhile, going forward, give every hard-drive [internal & external], every good partition, every usb device, a unique name, so that you will always know what your utility is going to be "aimed at". A couple of tools you might need: MiniTool Partition Wizard version 9.1, MiniTool Power Data Recovery, or any similar utilities with power to get the job done. Recovering those files is going to much like going to a large junk yard, spreading out a tarp, gathering from all over the parts of desired cars, and placing said pieces unto the tarp -- depending upon the partition(s) that existed, depending upon the "MFTs" and data folders within said partitions that existed -- before the accidental format -- data reconstruction might be remotely possible.
One more thing -- that format, was that format a Quick Format, or, was that format a Full Format? If Full Format, anything, everything, file-wise, that was overwritten before you turned off the computer is forever gone.