We want to find the value of $X$ in the given situation.
The question asks for half of the absolute value of the difference of the squares of $X$ and 16.
We can write this as an equation:
$\frac{1}{2} |X^2 - 16^2| = 34$
To find the value of $X$, we can solve for $X$ in this equation.
First, we can simplify the equation by calculating the difference of the squares:
$\frac{1}{2} |X^2 - 256| = 34$
Next, we can eliminate the absolute value by considering both the positive and negative cases.
Case 1: $X^2 - 256 = 34 * 2$
Simplifying, we have:
$X^2 - 256 = 68$
Adding 256 to both sides of the equation, we find:
$X^2 = 324$
Taking the square root of both sides of the equation, we get:
$X = \pm 18$
Case 2: $X^2 - 256 = -34 * 2$
Simplifying, we have:
$X^2 - 256 = -68$
Adding 256 to both sides of the equation, we find:
$X^2 = 188$
Taking the square root of both sides of the equation, we get:
$X = \pm \sqrt{188}$
Given that the value of $X$ is 18, we can conclude that $X = 18$.
The value of X is 18.
The answer is: 18
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
What is half of the absolute value of the difference of the squares of X and 16?
If we know the answer to the above question is 34, what is the value of unknown variable X?

### Answer:
