Hi Mike. My name is***** you for your question and the opportunity to assist.
Was your recent backup a full system image created with a program like Acronis True Image
or another similar program?
Unless your back up was made using third party software there won't be any way to return to Windows 8.1 without having and installation disk. Once Windows 8.1 is put back on the computer you'll be able to restore your backup.
In order to restore a backup the software that created it needs to be running first.
That is usually accomplished by booting from a CD containing the restore program.
If you created a backup using Windows 8.1 backup utility then you'd need to have Windows 8.1
running on the computer to do the restore.
Do you have a Windows 8 or 8.1 install disk?
Sorry for the delay. Do you have the 25 character product key for a retail version of Windows 8.1?