You will both lose, meaning the game will be a draw.
Your Eye for an Eye does resolve first, yes, but it doesn’t cause any damage when it resolves. All it does is set up a replacement effect that will happen the next time you would take damage this turn.
So Eye for an Eye resolves, and then Fireball resolves. When Fireball resolves, instead of just you taking 5 damage, you and your opponent both take 5 damage at the same time.
It would work the same if the damage were during combat. Your Eye for and Eye would resolve; setting up the replacement effect. Then when the creature would deal you damage, both you and your opponent take damage at the same time.
104.3b If a player’s life total is 0 or less, that player loses the game the next time a player would receive priority. (This is a state-based action. See rule 704.)
104.4a If all the players remaining in a game lose simultaneously, the game is a draw.
- State-Based Actions
704.3. Whenever a player would get priority (see rule 117, “Timing and Priority”), the game checks for any of the listed conditions for state-based actions, then performs all applicable state-based actions simultaneously as a single event.
704.5a If a player has 0 or less life, that player loses the game.