10.13 uses a new drive structure called APFS. If it is not a recognised format, a boot drive will need to be reformatted before it will recognise as a boot source.
Is the external drive for just data storage, or is it a boot drive as well?
If it is just an external drive for storing files, then the old partition structure is still recognised, in which case you likely have a fault with your external drive.
try it in a different machine to be sure, but you may have to look at data recovery if your hard drive is failing.