Let's break down the expression step by step:

The expression is:

$-|-14 + 2| + 58 - (-13) - 16$

1. Simplify inside the absolute value:

$-14 + 2 = -12$ Thus, the expression becomes: $-| -12 | + 58 - (-13) - 16$

2. Apply the absolute value: $|-12| = 12$ Now the expression becomes: $-12 + 58 - (-13) - 16$

3. Simplify the double negative: $- (-13) = +13$ Now the expression becomes: $-12 + 58 + 13 - 16$

4. Perform the arithmetic operations: $-12 + 58 = 46$ $46 + 13 = 59$ $59 - 16 = 43$

So, the final result is: $\boxed{43}$

Would you like further explanation or clarification on any step?

Here are some related questions you might find interesting:

1. How do absolute values affect equations?
2. What is the difference between adding and subtracting negative numbers?
3. How do you simplify expressions with multiple operations like this?
4. What is the order of operations in mathematics (PEMDAS)?
5. How do you handle double negatives in mathematical expressions?

Tip: When dealing with absolute values, always make sure to simplify the expression inside the absolute value first, then take the absolute value afterward!