It is best if you ask your teacher for details about what he or she wants to see. This is because different teachers could certainly have different things in mind when assigning a paper like this. What you write also depends on how long this paper has to be.
Without knowing more about the assignment, I would say that the first thing to do would be to explain the meanings of the mottos. This is more important, of course, for E Pluribus Unum than for “In God We Trust.” You could explain that the motto was meant to emphasize how the United States was made up of many different colonies/states that came together to form one country. This was a big deal in the early days of the country because the states sort of saw themselves as little separate countries more than as parts of one big country. You might discuss the idea that, in today’s world, we often think that this phrase refers to the idea of cultural diversity and the American “melting pot.”
Depending on what your teacher wants to see, you might talk about why “In God We Trust” became the official motto back in the 1950s. Historians typically say this was connected to the Cold War and the fact that communists were officially atheist. You might connect it to the fact that “under God” was added to the Pledge of Allegiance at that time.
Again depending on what your teacher wants, you might end with a discussion of which motto you think is better for the country.