First, we will need to re-write this word problem as a mathematical equation. We are told that "The sum of two times a number and two is ten", so we can use the variable "N" to stand for our mystery number and write:
2N + 2 = 10
This is because we are adding two times a number, or "2N" and the number "2" together to equal "10". Then we can use algebra to isolate our variable N. We subtract 2 from both sides of the equation to give us:
2N = 8
We can then divide both sides of the equation by 2 to completely isolate N, giving us our final answer:
N = 4
The number we are looking for is 4!