Check out The Difference Between “Both” and “Each.” by rogersgeorge. Here is an excerpt:
You need a context to be able to tell whether “each” refers to two things. For example, you could say that each hand has a glove on it, or each team member was in uniform.
Let’s assume the context implies two things. You still have an important difference between these two words:
“Both”…
The full article is available here.