Madrid Airport

It should be with the normal caution of being on time and if you don't have checked luggage. I, personally, would not book it that tight because you have little room for delay. Some airlines have a 45 min cut off for checkin so unless you can check in on line prior to leaving the states you might want to rethink this.

Are you arriving at and departing from the same terminal? Madrid Airport is pretty spread out, at least T4 is far from the others, and if you have to transfer between them it can take some time, in addition to the passport check, etc. Even if your Delta flight is right on time (which you can't predict or control) it seems tight. And since you are on separate tickets, if the Delta flight is late you are out of luck.

I would want more time... I LOVE Madrid. But the airport is not exactly a model of "efficency" If you have to check luggage it's not going to happen (and that may be true on both ends) And the standard "I travel carryon" has a warning. So does well over half the plane. I travel carry on weekly. Every flight Delta gate checks LOTS of luggage because the overheads are full! Realize that if Delta is late, you get held up in immigration or you have to take the bus to/from Terminal 4 you are at the mercy of AirEuropa who can easily tell you that the only way to get there is a full fare walkup ticket. I allow 4 hours on non-protected connections to try to minimize that risk...

You will have to go through passport control, retrieve your bags, walk from T1 to T2, recheck in with Air Europa, go thru security again (I'm pretty sure), get to your gate. You do not have to go out to T4. Doable in your time frame if Delta arrives on time & T2 security isn't too crazy.