Determining Values from Equations

Very Hard Data Sufficiency Determining Sufficiency

Let $x$ and $y$ be two positive integers. Determine the value of the expression $x^2 - y^2$.

Statement (1): $x + y = 10$.

Statement (2): $x - y = 2$.

Statement (1) alone is sufficient, but statement (2) alone is not sufficient.

Statement (2) alone is sufficient, but statement (1) alone is not sufficient.

Both statements (1) and (2) together are sufficient, but neither statement alone is sufficient.

Each statement alone is sufficient.

Statements (1) and (2) together are not sufficient.

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