Statement 1 is insufficient. Statement 1 tells us that the product of the two numbers is 21, which gives us the possible pairs: $(3,7)$ or $(1,21)$. However, this does not provide enough information to determine the unique pair of numbers, so Statement 1 alone is insufficient to answer the question.

Statement 2 is insufficient. Statement 2 tells us that the sum of the two numbers is 10, which gives us the possible pairs: $(1,9)$, $(2,8)$, $(3,7)$, $(4,6)$, $(5,5)$. While this narrows down the possibilities, it still does not uniquely identify the pair of numbers, so Statement 2 alone is insufficient to answer the question.

Statements 1 and 2 together: Sufficient. When combining both statements, we find that the only pair of numbers that satisfies both the conditions of having a product of 21 and a sum of 10 is $(3,7)$. Therefore, the statements together are sufficient to determine the two numbers.