Upvote:3
The airport website has a list of restaurants sorted by terminal and pre/post security. As pre-security restaurants in Terminal E, it lists the Dine Boston Restaurant and Cafe, described by Google as "Modern, informal spot with a New Englandβinspired menu, including thin-crust pizza & other pub grub". There is also a Dunkin Donuts.
You could also go to another terminal for more options. There is a free shuttle.