Hi David. I'm Greg, an installation specialist and 9 year Windows MVP, here to help you.
Yes, you would restart the PC to reinstall a driver you uninstall for that purpose.
If not then run the Hardware and Devices troubleshooter at Settings > Update & Security > Troubleshoot.
I'm not sure why the driver isn't posted under any OS on the Toshiba page for your model. Try your full model or serial number to refine it.
Try also tracing the hardware ID: http://answers.microsoft.com/en-us/windows/wiki...
I hope this helps. Feel free to ask back any questions and let us know how it goes. I will keep working with you until it's resolved.