If $8 < x < 9$, then $8^2 < x^2 < 9^2$.
Simplify to get: $64 < x^2 < 81$

Since $x^2 = (10 – y)(10 + y)$, we can substitute this value into the above inequality to get: $64 < (10 – y)(10 + y) < 81$
Expand to get: $64 < 100 – y^2 < 81$
Subtract $100$ from all sides to get: $-36 < –y^2 < -19$
Multiply all sides by $-1$ to get: $36 > y^2 > 19$ [since we multiplied all sides of the inequality by a NEGATIVE value, we REVERSED the direction of the inequality symbols]

At this point, we can easily see that $y = 5$ satisfies the inequality $36 > y^2 > 19$

Answer: E