If the computer is booting in EFI mode, then both the Ubuntu boot loader (GRUB 2, by default) and the Windows boot loader can reside on the same EFI System Partition (ESP). The ESP is a FAT partition that's intended for this purpose -- to hold boot loaders. Microsoft requires that manufacturers use EFI mode for pre-installed Windows 8 and later computers, so if the computer came with Windows 10, chances are it uses EFI mode and what you describe should work. The most likely explanation of the symptoms you're describing is a defective firmware, perhaps in conjunction with some misapplied fixes intended to overcome such defects.
OTOH, in BIOS mode, boot loader code goes in the Master Boot Record (MBR; aka the first sector of the hard disk) and in various follow-on locations. Typically, Windows boots from the MBR to the Partition Boot Record (PBR; aka the first sector of the partition) to files in the NTFS volume, whereas GRUB boots from the MBR to some post-MBR code to files in the Linux directory tree. If you install GRUB to a partition rather than to an MBR, though, it will take over the PBR. If you install GRUB to the PBR of a Windows partition, then that partition will no longer boot Windows. The symptoms are consistent with what you've reported, at least as far as I understand them. You're most likely to encounter a BIOS-booting Windows 10 on a system you've upgraded from Windows 7 or earlier, installed yourself from scratch, or re-installed yourself over an earlier installation. The solution to your problem in this case is likely to involve using Windows tools to restore the PBR (and probably the MBR), then re-installing GRUB to either the MBR or the PBR of an Ubuntu filesystem partition.
Because EFI-mode and BIOS-mode booting are so different, fixing your problem requires that you know which boot mode you're using. In Windows, boot mode is tied pretty tightly to partition table type, which you can determine in Ubuntu with:
sudo parted -l | grep Table
The output should specify your disk's partition table type, as in:
Partition Table: gpt
This indicates GPT, and therefore an EFI-mode boot of Windows. If it reads msdos rather than gpt, then that indicates MBR, and therefore a BIOS-mode boot of Windows.
If you can't get it fixed once you know the boot mode, please run the Boot Info Script on your system. This will produce a file called RESULTS.txt. Post it to a pastebin site and post the URL to your document here. This will give us additional diagnostic information. Also, please specify the make and model of your computer.
