Τρώω shows an action that happens continuously. On the other hand φάω shows that I'll eat it only once. So you need the verb tense that shows you'll eat the sandwich more than once in the future. So, I believe that's why "eating" is more correct than "eat". A question rises now. Would "I will be eating the sandwich" be correct?
But then, εγώ μπορώ να τρώω ένα σάντουιτς για μια ώρα (I can be eating a sandwich over an hour/for an hour), if I take small bites, or if I do breaks, or if I'm doing other stuff while eating the sandwich.
On the other hand, εγώ θα φάω ένα σάντουιτς και μετά θα δουλέψω (I'll eat a sandwich and then I'll work). In this case, we may too eat the sandwich in a relaxed manner, and not in an instant, but the phrase "θα φάω" gives the impression that it won't take much time. So one can assume that it'll be just like an instant.
Why was "I will eat the sandwich" marked as incorrect? It's an action to take place in the future in English and since it is a temporal action (beginning and ending likely in a relatively short period of time), I'm baffled as to why it wouldn't mean the same thing as "I will be eating the sandwich."
Continuous future = θα + cont.stem with present endings: θα το διαβάζω/ I am going to read it (a lot), θα τρώω/ I will eat a lot
Simple future = θα + simple stem with present endings: θα το διαβάσω/ I will read it (just once or so), θα φάω/ I will eat (τρώω is irregular)
see more in http://www.foundalis.com/lan/grkverbs.htm