Diophantine Equation

We have $$\displaystyle x,y\in\mathbb N_0$$ and

$\displaystyle x-y=x^2+xy+y^2$

The solutions are $$\displaystyle (x_1,y_1),(x_2,y_2),\ldots,(x_n,y_n)$$.

Find $$\displaystyle \sum_{i=1}^n(x_i+y_i)$$.

×