I accidently wrote over my external driveFollow

The good news is yes, it's probably recoverable. You will need an undelete software to recover it. I use a copy of this one. http://www.lsoft.net/undelete.aspx it's not free, but it works well and is simple and easy to use. Also you can download it electronically. You can also try testdisk photorec if you want a free one, but its command line. there are plenty of others out there too.

The tricky part here is how much of your drive you will be able to recover. when you format and reinstall a drive like that, what really happens is that the hard drive master records get told "there is no file there, ignore it, treat it as empty space" It doesn't go an "un write" the file. It's still there. until you write something over the top of it. so you are on a race against the clock. power down and unplug the external drive for now, then install the undelete software on the main installation. you want to wait to bring up the external drive until you are ready to start the recovery.

You will also need empty space as large as the data you are recovering to write it back to. You can recover it back to the same spot it started out at, but I don't reccommend this as it can damage your chances of future recovery if something goes wrong on the first try. Sometimes one file is toast and causes a recovery to fail, but the rest of the files in that pass are intact and will work if you retry.

Once you get everything recovered, take a look at the sticky in here and the section on backup drives, now that you know for a fact you need a better backup system. though admittedly in that specific scenario it wouldn't have helped as much

if you need any specific pointers on the restore process, feel free to PM me.