Implicit depreciation rate problem

Question

Suppose there is an infinitely-lived asset. Each period it depreciates so that if its value at time $t$ is $y_t$, then its value at time $t+1$ is $(1-\delta)y_{t}$ where $\delta \in (0,1)$ is the depreciation rate. The price charged for use of the asset is defined as the arithmetic sum of the values of the asset across all periods during which the asset is used (including today's period). Suppose $R$ is the rental price of using the asset for $T$ periods, while $P$ is the price of purchasing the asset (i.e. using it for infinitely many periods). $R, T,$ and $P$ are fixed and known. I am trying to find the implicit depreciation rate $\delta$ to justify these prices. I know that if $Y$ is the value of the asset today (unknown), $R=Y+(1-\delta)Y+(1-\delta)^2Y+...+(1-\delta)^TY$, while $P=Y+(1-\delta)Y+(1-\delta)^2Y+...$ This looks like a complicated system of equations to solve. I notice that $P=R+(1-\delta)^{T+1}(R+(1-\delta)^{T+1}(R+...))$, which eliminates $Y$ but I am not sure if this helps, or if there is another way to manipulate the two equations. Any thoughts on how to approach this are appreciated.