Rule for getting rid of absolute value bars "|  |"

1.  If there is a positive number between the "|   |", 
    change the bars to parentheses and proceed.

2.  If there is a negative number between the "|   |",
    change the negative sign on the number between the 
    bars to positive and then change the bars to 
    parentheses and proceed.

You got to here:     

|7| - |-10|

Look inside the first pair of absolute value bars.
You see a 7.  A 7 is positive so rule 1 applies, and
you just change the bars to parentheses:

(7) - |-10|

Now look inside the only remaining pair of absolute
value bars.  You see a -10.  A -10 is negative so rule 
2 applies, and you first change the -10 to +10, or just
10

(7) - |10|

Then change the bars to parentheses:

{7) - (10)

Now you don't need the parentheses, so you just have

7 - 10

which is 

-3

Edwin