The term you're looking to use is "absolute value."
Imagine the number line as a single axis of a graph plane; a dimension, rather. Number lines are commonly represented in whole numbers, each number representing a scaling increment of that line. Counting the total, positive amount increments between two numbers on the same number line will give you a hands-on approach at discovering absolute value. Absolute value looks like this:
$|-4| = 4$
$|9| = 9$
Positive and negative numbers come out as positive after determining absolute value.
Like usual, a number line will have negative numbers (numbers less than 0) to the left of 0, and positive numbers (numbers greater than 0) to the right of 0. Imagine a placeholder on your starting number which we'll say is $-5$. When subtracting a positive number from any number in this case, you will move your placeholder left. Subtracting $3$ from $-5$ will move your starting placeholder left two increments to $-8$.
Conversely, subtracting a negative number from any number becomes addition. If our placeholder starts on $3$, this will move it to the right towards more positive numbers. When subtracting $-5$ from $3$, we tell $3$ to no longer be burdened by losing $5$ from its value, and so the $-5$ is taken away.
I hope this paints a decent picture. I can edit this later with some Photoshopped number lines and other visuals if need be.