Is there any hope to find the general function $f(x,y)$ if we know the function value at two points as given?

Question

I am looking for a general function $f(x,y)$ for which I have

$$ (x_0,y_0)=(3,1) \quad \text{we have} \quad f(x_0,y_0)=12 $$ and $$ (x_1,y_1)=(5,1) \quad \text{we have} \quad f(x_1,y_1)=5(23-\sqrt{5})$$

Are these data sufficient to find such a function?