You don’t have to reinstall all Win, you could repair your boot/EFI via Diskpart.
You run your usb or win10 cd as you will install it then you look at bottom left Repair computer click on it and choose first option repair then in advanced option you will see to open Terminal command.C:/
In this terminal :
diskpart
Now list your disk :
list disk
Select the (x) concerned disk that contains your win 10 :
select disk x
Now that your disk is selected see the volumes inside it with :
list volume
Select your good (x) volume C: :
select volume x
Then see all partitions in this volume with :
list partition
If your EFI is not here just create it :
create partition efi
Check that partition named system is here :
list partition
You could format it now :
format fs=fat32 quick
Then quit Diskpart
exit
Finally on x:\Sources> repair your boit with :
bcdboot C:\windows
Now quit the terminal command to come back on win option :
exit
And click continue to boot your win10