I updated the BIOS to 1401 by using the USB method as (I think) is better as avoids any issues with Anti-Virus software.
The best thing to do is always be sure to download from the correct place ->
https://www.asus.com/uk/Motherboards/ROG-STRIX-Z390-E-GAMING/HelpDesk_BIOS/. I updated the BIOS first then the ME SW. One thing you can do if AV could get in the way of the install, is to download the package, then use 'msconfig' to do a 'selective startup' with only the Microsoft services running (do disable network interfaces first - so 'airplane mode'), reboot and install, then 'msconfig' again to get back to 'normal startup'.
One thing I found after installing the ME firmware was there was no way of telling if it worked, however, Intel provide a tool that will tell you the version, please see my post:
https://rog.asus.com/forum/showthread.php?115786-z390-e-ME-Firmware-update.