Couple alternatives....

Regular formula:
=MAX(INDEX(I2:I27+J2:J27,0))

Good point! Don't know why, but I seem to instinctively reach for the
catch-all SUMPRODUCT function without spending more time thinking about the
already array equipped ones.

or
Array Formula (with built in reminder)
=MAX(I2:I27+J2:J27)+N("Ctrl+Shift+Enter")

Hey! That's a good idea (although if the user is not familiar with the N
function, it might confuse him/her as well).

Rick