Let $x,y,z$ the numbers. From hypothesis we have $(x+y+z)^2=x^2+y^2+z^2$ and $xy=z^2$ The first equality is equivalent to $xy+yz+zx=0$ which combined with the second one gives $z^2+yz+zx=0$ or $z(x+y+z)=0$ so either $z=0$ or $x+y+z=0$. If $z=0$ then $x=0$ or $y=0$ If $x+y+z=0$ from the first part we get $x^2+y^2+z^2=0$ that is $x=y=z=0$ finally $(x,y,z)=(0,0,0),\ (0,k,0),\ (l,0,0)$