Is a verbal agreeement with an email for back-up a legal contract?

Generally speaking, contracts can be oral or written, except under certain circumstances such as the purchase of real property.  That type of transaction would violate the Statute of FRaud laws in your state and pretty much all states.  So it depends on the type of agreement.  Now, the use of email to "prove" a contract is not widely accepted because email accounts can be hacked.  How the court views the "evidence" varies from state to state.  Good luck.