Difference of Cubes Ratio

Let the numbers be $a$ and $b$, with $ab = 616$. $\frac{a^3 - b^3}{(a - b)^3} = \frac{157}{3} \implies \frac{(a-b)(a^2+ab+b^2)}{(a-b)^3} = \frac{(a-b)^2 + 3ab}{(a-b)^2} = 1 + \frac{3ab}{(a-b)^2} = \frac{157}{3}$. $\frac{3ab}{(a-b)^2} = \frac{154}{3} \implies \frac{3(616)}{(a-b)^2} = \frac{154}{3} \implies (a-b)^2 = \frac{9 \times 616}{154} = 9 \times 4 = 36$. $a - b = 6$. $(a + b)^2 = (a - b)^2 + 4ab = 36 + 4(616) = 36 + 2464 = 2500 \implies a + b = 50$.