316. $\left\{\begin{array}{l}(x+y)\left(x^{2}+y^{2}\right)=539200 \\ (x-y)\left(x^{2}-y^{2}\right)=78400 .\end{array}\right.$
316. Instruction. Dividing the 1st equation by the 2nd:

$$
\frac{x^{2}+y^{2}}{(1-y)^{2}}=\frac{337}{49}
$$

from which

$$
674 x y=288 x^{2}+288 y^{2}
$$

or

$$
98 x y=288(x-y)^{2}
$$

$$
\frac{(x-y)^{2}}{x y}=\frac{49}{144}=\frac{x}{y}+\frac{y}{x}-2
$$

$$
\frac{x}{y}+\frac{y}{x}=\frac{337}{144}
$$

let

$$
\frac{x}{y}=z
$$

$10^{*}$
rorдa

$$
144 z^{2}-337 z+144=0
$$

from which

$$
z=\frac{16}{9}
$$

Now it is easy to find:

$$
x=64 ; y=36
$$