How do you solve #sqrt(x^2 + 4) -sqrt(x + 10) = 0#?
Notice that you are dealing with the difference of two terms, which can only be equal to zero if the two terms in question are equal to each other.
This means that you can write
Your possible solution(s) must satisfy the condition
So, you need
Square both sides of the equation to get rid of the radicals
Move all the terms to one side of the equation and use the quadratic formula to determine the two solutions
Since both values satisfy the condition