Well since the Kentico doesn't know anything about the external domain it can't validate the authentication by itself.
So you'll be needing something custom. Do you have access to anything on the second server? As in can you customize code or add additional logic? Perhaps you can create a hook for Kentico to check if a user is logged on. Have a look at the documentation for managing external authentication and there is a link in there with code samples on how to handle custom external authentication. This should give you a starting point.
If that's not possible but you can add customization you could also let successful authenticated users be forwarded to your Kentico-domain with some additional unique and hashed parameters. And handle the check on your end. But since security is such an important topic and can have big consequences I would think about this carefully and consult with some security specialist before creating a custom authentication process.