optimizing Average Run Length of synthetic control chart

How can I code in R to solve for p in 370=(1/p)(1/[1-(1-p)^L]),L=1,2,3,......; and get the positive values of p at different values of L even when p is at the right hand side of the equation. Note that For L=1 it becomes 370=(1/p)(1/p) and hence p=0.0027.