Assuming you're starting from the usual open G, the tuning for open E would be this:
5th string -- e/g# (tuned down 2 frets or up one fret)
4th string -- E (tuned up 2 frets)
3rd string -- G# (tuned up one fret)
2nd string -- B (leave it alone)
1st string -- E (tuned up 2 frets)

that's really just open D raised one full step (or capoed). Some people tune the 5th string to a when playing open D, but it'll probably break if you try to raise it to b to match an E tuning, so e or g# is better; either of them works.

Tuning for open E minor is similar:
5th string -- e/g (tune down to E or leave at G; either works)
4th string -- E (tuned up 2 frets)
3rd string -- G (leave it alone)
2nd string -- B (leave it alone)
1st string -- E (tuned up 2 frets)