How can one find the value of x such that $\left(1-\sqrt{1-(R-1)^2}\right)-\left(1-R^{\frac{1}{2-x}}\right)^{2-x}=0$, $(0<R<1)$?

Question

How can one find the value of x such that $\left(1-\sqrt{1-(R-1)^2}\right)-\left(1-R^{\frac{1}{2-x}}\right)^{2-x}=0$, $(0<R<1)$?

some ideas so far are:

Choosing $R=0.5$,

$$0.133975\, -\left(1-0.5^{\frac{1}{2-x}}\right)^{2-x}=0$$

This would leave expanding the power $2-x$, but then it is unclear how to proceed.

Is there a method/technique to determine if this is possible without approximating $x\approx0.222052962563297$