You can use these instructions to create a bootable USB drive with GRUB that can run the Windows 10 installer. I used Arch Linux to prepare my USB device, but any Linux variant like Debian or Ubuntu should work.

I am assuming you have an appropriately large USB disk at /dev/sdz that you can completely erase for this process.

Unmount the USB drive if mounted.

sudo umount /dev/sdz*

Wipe all partitions from the USB device.

sudo dd if=/dev/zero of=/dev/sdz bs=512 count=1 conv=notrunc

Use sfdisk to create two partitions. The first partition will be a 500MiB bootable (*) Linux partition and the second partition will be an ntfs partition (7) that takes up the remaining space.

sudo sfdisk /dev/sdz << EOF
,500M,,*
,,7,;
EOF

Format the first partition, /dev/sdz1 as ext4.

sudo mkfs.ext4 /dev/sdz1

Format the second partition, /dev/sdz2 as ntfs.

sudo mkfs.ntfs /dev/sdz2

Mount /dev/sdz1 somewhere local. In my case, I am using /mnt/part1.

sudo mount /dev/sdz1 /mnt/part1

Mount /dev/sdz2 somewhere local. In my case, I am using /mnt/part2.

sudo mount /dev/sdz2 /mnt/part2

Mount your Windows 10 installation ISO. In my case, I am mounting it at /mnt/win10.

mount -t udf ~/win10.iso /mnt/win10

Install grub to the ext4 partition (sdz1). This command provides a minimal GRUB install inspired by an Arch Linux article.

I will admit I don't entirely know what each module here does, but I chose a minimal list that seemed to be needed for my configuration.

sudo grub-install \
    --no-floppy \
    --target=i386-pc \
    --recheck \
    --debug \
    --locales="en@quot" \
    --themes="" \
    --root-directory=/mnt/part1 \
    --boot-directory=/mnt/part1/grub-boot \
    --install-modules="ntldr normal search ntfs" \
    /dev/sdz

Create a grub.cfg GRUB configuration file at /mnt/part1/grub-boot/grub/grub.cfg. Here is a relatively minimal grub.cfg based on a few articles.

# USB Device:/grub-boot/grub/grub.cfg

set timeout=10 set default=0

menuentry "Windows 10 Installer" {
    insmod ntfs
    search --set=root --file /bootmgr
    ntldr /bootmgr
    boot
}

Copy Windows 10 installation files to the ntfs partition (sdz2).

rsync -vr /mnt/win10/ /mnt/part2/

Sync files to the device. Depending on the speed of your device, this may take some time.

sync

Clean up.

sudo umount /dev/sdz*

Boot! You should be all set to go at this point.

If, when booting to Windows 10 from the USB device, you encounter an error saying this:

A media driver your computer needs is missing. This could be a DVD, USB or Hard disk driver. If you have a CD, DVD, or USB flash drive with the driver on it, please insert it now.

Note: If the installation media for Windows is in the DVD drive or on a USB drive, you can safely remove it for this step.

then you may want to look at a Microsoft Community article addressing that issue. You may also want to verify that all the files copied properly during rsync or re-copy the files anyway just in case something was corrupt. You may also want to verify the integrity of the source Windows 10 iso file. Finally, I found that USB 2.0 drivers worked far more reliably for me than USB 3.0, and resolved that error when I encountered it on one of my machines.