This is what WD has to say about this problem:
Thank You for contacting Western Digital Customer Support my name is Cedrik and I am one of the WD Support Agents.
First and foremost, we would like to Thank You for taking the time to contact us in regards to the issue with My Book World Edition II (white light). I sincerely apologise for any inconveniences that this may have caused You.
If I understood correctly after You upgraded to Windows 10 the WD Anywhere Backup software does not work and You can still access the device form the file explorer.
I am sorry, but the My Book World Edition II is a legacy product as well as the software. It will not work on Windows 10. However the My Book World can still be used and accessed with the file manager. You can back up Your data manually by dragging and dropping it into the My Book World folder.
Can You recover Your files using the file manager?
If not. Could you get a computer with Windows 7 on it and use it to recover your backup?
I hope this information resolves Your issue if the issue is not resolved and You require further assistance, please reply.