Thomas Rushton has a script for us:
Why Script This? What’s Wrong With SSMS’s GUI?
Well, although SSMS does allow you to look at the error logs, it’s not very helpful for filtering – you can only filter for items that match, rather than exclude items. There are a few other filters as well – I guess the whole thing is just a wrapper around xp_readerrorlog below…
But Thomas has a better way for us.