I am trying to prove a high-probability bound which amounts to choosing $M > 0$ and $W>0$ such that for any fixed $\delta \in (0,1)$, we have
$$(1-\delta/W)(1-T(2\delta/W + c^M)) > 1- \delta,$$
where $c = \Phi(1) = 0.8413$ and $\Phi(x)$ is the cumulative distribution function (CDF) of the standard normal distribution. Here $T > 1$ is a positive integer. How can I choose $W$ and $M$ which would satisfy this? It's okay if $M$ and $W$ depends on other variables in the equation such as $T$, $c$.
It's okay if $W$ takes something of the form $\text{constant}\times MT$.