Repair Windows 10 boot loader
Assuming Windows is installed to GPT disk.
To successfully boot Windows 10 (also Windows 8.1/8/7) on UEFI firmware you need exactly 3 partitions on a GPT styled disk:
EFI System partition (usually 100 MB - 500 MB)
Microsoft Reserved partition (exactly 128 MB)
Windows partition (at least 20 GB for 64-bit Windows)
Eventually you could have a separate "recovery" partition.
The presence of first three partition mentioned is mandatory or else Windows cannot boot.
The command to fix BCD + boot loader + boot manager and write a boot entry in NVRAM is bcdboot.exe -
bcdboot N:\Windows /s Z:
where N: is Windows partition and Z: is EFI System partition. (Later you have to fix recovery loader separately using ReAgentC.exe command.)
You can use also bootrec.exe command from recovery environment to fix booting (not always successful but fixes also recovery loader).
No need to say that you have to boot Windows installation/recovery media (USB/DVD) using EFI boot.
UEFI booting does not use MBR and partition boot records for booting but it may help to rewrite MBR (should be a protective MBR on GPT disk) using bootsect.exe command in case MBR was tampered by Linux install. Windows does not like "mixed" MBR format on GPT disk.
Reference: Repair Windows BCD on UEFI and BIOS
Hope this helps.