The parallel lines create similar triangles. Which means sides are proportional...
[tex] \frac{BR}{CS} = \frac{AR}{AS} [/tex]
[tex] \frac{BR}{CS} = \frac{10}{14} = \frac{5}{7} [/tex]
So if then the ratio of AR to AS = 5/7
Create a proportion with the other similar triangle that contains the shared side:
[tex] \frac{5}{7} = \frac{e}{18} [/tex]
Cross multiply
e = [tex] \frac{90}{7}=12 \frac{6}{7} [/tex]