Try the following, which works in Windows 7 and 8, but I can't promise anything with 10:
- Open an Administrator Command Prompt window by right-clicking the Command Prompt icon and selecting the option to run it as Administrator.
- In the Command Prompt window, type
mountvol P: /S. (You can change
P: to any unused drive letter; that's arbitrary.)
- Use the Command Prompt window to access the
P: (EFI System Partition, or ESP) volume.
You'll need to use text-mode commands, rather than the GUI, but this method should work.
Another alternative is to use another OS. Even if you can't boot your other OS now, which you strongly imply, you might be able to use an emergency disk. An Ubuntu installation medium, for instance, should let you access the ESP pretty easily. IIRC, it should show up as a volume in the lower-left corner of the screen; or you can use the standard Linux
mount command to mount it in any way you like.