Automatic Login from one web site to Moodle web site?

I have a portal called `www.example.com` and a Moodle site called `moodle.example.com`. I have some users on both sites, which have the same usernames and passwords. What I want is when a user logs in on non-Moodle site called www.example.com after clicking some link, he should auto login to the same user on moodle.example.com. Is there any way to do this?