Answer:
[tex]k=7; k=13[/tex]
Fast and loose:
If you stare at it for a while, you can see that the LHS is the distance between k and 10. Basically, you've asked to pick k so you get two numbers that are 3 apart from 10. And these two numbers are 7 to the left, and 13 to the right.
Rigorously
Split it in 2 situations, depending if the quantity inside the absolute value is greater or smaller than zero.
If it's greater or equal than zero:
[tex]\left \{ {{k-10\geq 0 } \atop {k-10 = 3} \right. \\\left \{ {{k\geq 10 } \atop {k = 13} \right.[/tex]
And since 13 is indeed greater than 10, it's a valid solution, so you get the first one. For the second, you assume negative values for the quantity inside, and change sign:
[tex]\left \{ {{k-10 < 0 } \atop {k-10 = -3} \right. \\\left \{ {{k < 10 } \atop {k= 7} \right.[/tex]
In this case, 7 is a valid solution too since it's less than 10
