$x,y-\text{szukane liczby}$  

$\text{Załoˊz˙my, z˙e x}>\text{y}.$  

$y=x-4$  

 

$x^2+{\left(x-4\right)}^2=400$  

$x^2+x^2-8x+16=400$  

$2x^2-8x-384=0$  

$x^2-4x-192=0$  

 

$\Delta =16+768=784$    

$\sqrt{\Delta }=28$  

 

$x_1=\frac{4+28}{2}=16$  

$x_2=\frac{4-28}{2}=-12$   

 

$\{\begin{array}{l}{x}_1=16\\ y_1=x_1-4\end{array}\vee \{\begin{array}{l}{x}_2=-12\\ y_2=x_2-4\end{array}$  

$\{\begin{array}{l}{x}_1=16\\ y_1=12\end{array}\vee \{\begin{array}{l}{x}_2=-12\\ y_2=-16\end{array}$