To solve this expression, we need to calculate the exponent first, then perform the addition and subtraction.

First, let's calculate 2 raised to the power of 3.3.5:

2^3.3.5 = 2^(3.5) = 11.3137

Now, let's perform the addition and subtraction:

17.85 + 17.15 - 11.3137 = 23.6863

Therefore, the result is approximately 23.6863.