Thanks,
I made a System Image Backup of my hard drive this morning. Then I booted the computer with the Windows 10 install media (USB flash drive). I went to Advance Options, then System Image Recovery. Look at post #101. You posted a picture of the screen it took me to. All you have to do is click on "TOSHIBA EXT", it turned blue, and I was able to click Next at the bottom of the window. Just click on it once. Don't double click. If it doesn't turn blue the first time, try clicking on it again, but don't double click. Give it a try.
Don't click on the Advanced button. That does nothing for us. The first option is for people who have a network and store their image on it. You would use the second option if your portable hard drive needed a driver for Windows to recognize it. Windows does not need a driver to see you Toshiba drive.