Error 0x80070570 while installing Windows 10

I'm following this answer to install Windows 10 on a new drive.

I created a bootable USB drive using the Win10_1803_English_x64.iso image, once with WoeUSB, and once manually, but the installation failed each time. The result was the following error message at around the 10% mark:

Windows cannot install required files. The file may be corrupt or missing. Make sure all files required are available, and restart the installation. Error code : 0x80075070

The ISO file seems to be valid - I've checked its checksum.

How can I complete the installation?