Accidentally reformatted external hard drive

Hello,
I really appreciate your help!

i accidentally formatted an external hard drive that was still attached to my computer while re-formatting the internal hard drive. I am trying to recover the data, but cannot even view the external hard drive anymore when I click on 'Computer'. The hard drive does show up in Disk Management screen, but it shows as unallocated and no drive designation. Could you please help me understand how I get my computer to recognize the external hard drive? or how I can assign a drive letter to it?

Thanks in advance for anything you can do to help.