ANSWER
The two numbers are 128 and 128
Step-by-step explanation
Let the two numbers be x and y.
We have that:

where A is a maximum.
From the first equation:

Substitute that into the second equation:

The equation above is a quadratic equation in the general form:

The parabola is downward facing and so, its vertex will be the maximum.
We can find the vertex (x, y) of the parabola by using:

In the case given, the vertex can be found by using:

Recall that:

Therefore, we have that:

Hence, the two numbers are 128 and 128.