Arithmetical representation $F(x,y,z)Longleftrightarrow (x+z)=y lor (y+z)=x$


I am kind of confused which function $f:mathbb{N}^2longrightarrowmathbb{N}$
is presented by $F(x,y,z)Longleftrightarrow (x+z)=y lor (y+z)=x$

I know that $f(x,y)=y-x$ is represented by $F(x,y,z)Longleftrightarrow (x+z=y)lor ((z=0)land exists w(x+w)=y)$

But the or symbol confuses me … My guess was
$f(x,y)=max{x-y,y-x}$ but i think this is wrong due to a missing check in F(x,y,z)