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” refers to two things together.
“Each” refers to two things separately.
Here’s a good example of getting it wrong:
There is one [polar vortex] at both poles, and other planets have them too.
Sorry, each pole gets its own vortex.
Just for grins, here’s a Hubble photo of Saturn’s polar vortex.