154. $\left\{\begin{aligned} x^{2}+y^{2} & =a^{2} \\ x-y & =b\end{aligned}\right.$
154. The second equation is squared:

$$
x^{2}+y^{2}-2 x y=b^{2}
$$

therefore,

$$
a^{2}-b^{2}=2 x y ; 2 a^{2}-b^{2}=(x+y)^{2} ; \quad x+y=\sqrt{2 a^{2}-b^{2}}
$$

from here we find $x$ and $y$.