Thanks for the great puzzles! I found a second answer! A quick rearrangement of the equation provides m= 2^(m/32) which can be interated using a calculator or Python...

```

m = 1

for i in range(10):

m = 2**(m/32)

print(m)

```

And this results in 1.0223929402057803

Plugging it back in to the two terms verifies it.

You can start m with just about any number, including zero.