Passing Login Information to External Site


I am trying to figure out if this is possible I have a private WordPress site with a bunch of members I also have another that is not wordpress based. I want to have a link that a user can click on that would send them over to this different portal and pass their login information over.

The url would look something like this:

When I fill in the UserID spot and Password spot manually the login works. But i want to be able to pass the user information from wordpress into the url so that it would automatically log them in.