Determine the point(s) where the two equations intersect: $\begin{array}{l}y=x^{2}+10 x-18 \\ y=2 x+2\end{array}$

Step 1 ：Set the two equations equal to each other: \(x^{2}+10 x-18 = 2x + 2\)

Step 2 ：Solve the equation for x to get the x-values of the intersection points: \(x = -10, 2\)

Step 3 ：Substitute the x-values into either of the original equations to find the corresponding y-values: \(y = -18, 6\)

Step 4 ：Final Answer: The points of intersection are \(\boxed{(-10, -18)}\) and \(\boxed{(2, 6)}\)