Use sharepoint credentials for sso with third party

Use sharepoint credentials for sso with third party

I was drowning in the information available on sharepoint sso, so I'm
asking this question to see if I want is even possible...
At the company I work at we use office 365/sharepoint and some other
programs/websites hosted elsewhere. One of those websites is a homemade
website to manage worked hours, schedules and stuff like that; this is the
website I'm trying to use the sharepoint credentials on.
The website is build in PHP, uses a mysql database and has it's own login
with your email address as user name. The thing I'm trying to do here is
automatically sign people in on this website if they're logged in on
sharepoint based on their email address.
Some additional info:
Not using Windows Azure
The website doesn't run on a Windows server
Is it possible to do this?