@Lahiri I might try two different approaches:
Flash a Solus ISO to a USB and boot up. Run the Solus installer and try to point it at your new EFI partition (make sure to preserve the Windows one, I've been able to do something similar by clearing the "boot" flag on the EFI that belongs to the different OS, then after install, open up gparted and restore the flag), then I would see if you can just "use" the current installation of Solus as your OS. You would have to do manual partitioning scheme in order to do that, rather than the guided (entire disk) setup.
Or you could try to install Solus to a different machine and then copy the EFI partition to an external source. Then I would try to mount the old file system (again with the Solus USB) and copy the contents of the EFI partition that was freshly installed from the fresh install you just did. I have no idea if that works, though, and I'm sure there is magic going on in the background to set up an EFI partition, so you may have to edit some files or whatnot 🙁 Sorry I couldn't be more help.