Let's use the variables x and y to represent the two numbers.
If the quotient is 2 and the product is 128, we have:
[tex]\begin{gathered} \begin{cases}\frac{x}{y}=2 \\ xy=128\end{cases} \\ \\ \frac{x}{y}=2\to x=2y \\ \\ xy=128 \\ (2y)y=128 \\ 2y^2=128 \\ y^2=64 \\ y=\pm8 \\ \\ y=8\to x=2\cdot8=16 \\ y=-8\to x=2\cdot(-8)=-16 \end{gathered}[/tex]So the numbers can be 16 and 8 or -16 and -8.
