Single Choice Early Action

Can I apply early to both MIT and Yale?

No. See: http://admissions.yale.edu/faq/single-choice-early-action

As MIT does not have rolling admissions, nor does it have early decision (ED) or is it a public institution, and it isn’t an institution outside of the U.S., you cannot apply SCEA to Yale and EA to MIT. You must apply to one or the other.

That said, if you apply to MIT you can apply to many other non-binding schools EA (just not Yale).