- 1. A.

By adding the two equations, we get
$$
\begin{array}{l}
(x-y)^{2}+(x-y)-2070=0 \\
\Rightarrow x-y=-46 \text { or } 45 .
\end{array}
$$

Therefore, the sum of all possible values of $x-y$ is -1.
1. If $x^{2}-x y+x=2018, y^{2}-x y-y=52$, then the sum of all possible values of $x-y$ is ( ).
(A) -1
(B) 0
(C) 1
(D) 2018