When a Windows 10 update breaks the dual boot

Execute the following commands using a LiveCD:

sudo mount /dev/sdXY /mnt
sudo mount /dev/sdXX /mnt/boot/efi
for i in /dev /dev/pts /proc /sys /run; do sudo mount -B $i /mnt$i; done
sudo chroot /mnt
grub-install /dev/sdX
update-grub

Note that X and Y are only used as an example. E.g. it can be that the EFI system partition is on a completely different disk (hard drive) than the Linux system, which needs to be repaired.