If you think your install in sda10 is just missing some files you can chroot into it and update it. I show updating grub but I do not know if other updates are required.

sudo mount /dev/sda10 /mnt
sudo mount --bind /dev /mnt/dev
sudo mount --bind /proc /mnt/proc
sudo cp /etc/resolv.conf /mnt/etc/resolv.conf #(may or may not be necessary to establish an internet connection)
sudo chroot /mnt
#Then run whatever commands needed - no sudo needed (maybe good to run "df- H" and "cat /etc/issue" to be certain you mounted the correct partition).
apt-get remove grub
apt-get install grub
apt-get update
apt-get upgrade
#When done:
exit
sudo umount /mnt/dev
sudo umount /mnt/proc
sudo umount /mnt