How did you manage to get your pawn to h3?!
I'm assuming the position you're interested in occurs after 1. e4 e5 2. Nf3 d5. Now white's best move is considered to be 3. exd5. After 3...e4 4. Qe2 Nf6 5. Nc3, white regains the pawn on e4 leaving black with little to no compensation. Feel free to explore the lines yourself, but that's the gist of it as far as I can tell.
In a more general sense, have a little faith in your position :) You seem to be already worried about defense...but all white has done so far is make the absolute most classical, principled opening moves. Why on earth does black get to make this super-aggressive thrust in the center? White should be looking to go on the offensive and punish this overreach.
For a little inspiration, check out a Tal classic.