It's not clear if you've installed in BIOS mode or in EFI mode. If the latter, "update-grub" should theoretically get it working; but GRUB's Windows boot stanzas sometimes fail, so this method might fail. There are numerous examples on the Web of alternatives you can add to /etc/grub.d/40_custom, but they're all rather hit-or-miss -- what works for one computer fails on another. Alternatively, you could install my rEFInd
boot manager, which can boot Windows or Linux (even without GRUB).
If you've installed Linux in BIOS mode, the trick will be to get it booting in EFI mode, since switching between BIOS-mode and EFI-mode boots is awkward on most computers. There are a number of ways to do this. The easiest are to use Ubuntu's "Boot Repair" tool or to install rEFInd from Mint. In either case, you may need to fiddle with your firmware settings to get the computer to boot in EFI mode rather than in BIOS mode.
To determine your current Linux boot mode, look for a directory called /sys/firmware/efi. If it's present, you've booted in EFI mode; if not, you've probably
booted in BIOS mode.