AMC 12 2023b Problem 10

In the $xy$-plane, a circle of radius $4$ with center on the positive $x$-axis is tangent to the $y$-axis at the origin, and a circle with radius $10$ with center on the positive $y$-axis is tangent to the $x$-axis at the origin. What is the slope of the line passing through the two points at which these circles intersect?

\textbf{(A)}\ \dfrac{2}{7} \textbf{(B)}\ \dfrac{3}{7} \textbf{(C)}\ \dfrac{2}{\sqrt{29}} \textbf{(D)}\ \dfrac{1}{\sqrt{29}} \textbf{(E)}\ \dfrac{2}{5}