Wow, I did not know that Springsteen is holding an Esquire on the Born to Run album cover. I never really looked closely at that guitar until you mentioned it. It looks like a standard Telecaster and so that is what I thought it was. A close look though shows it says Esquire on the headstock. I read a bit about that and it seems that the explanation may be that the body is from a Telecaster (it looks like it is but the Esquire had the same body shape) because you can see the normal lipstick pick-up in the neck position and the single coil at the bridge but the neck is from his Esquire which he swapped out onto a Telecaster body. However, there is something that is a mystery taking place between those two pick-ups and it looks like he had a third pick-up added between them. A middle pick-up...but it looks a bit funky in the photos. I am trying to get a closer look at it. 

Both Springsteen and the guitar are iconic, no doubt. I think over the years I have only really seen him playing a Telecaster type guitar and that was all he played when I saw him live at the Garden this year.