The Q10 runs from the Union Turnpike Station on E/F. However, not all Q10's go into JFK (the bus has to marked JFK; the route makes many stops and takes at least 45 minutes (if there is no traffic.) I've tried that route several times and will not do it again!
[There is a Q10A which runs for about a 1 hour period on weekday mornings that runs non stop from Union Tpke to JFK...at least that is what the schedules state.)