Let's define the two consecutive even integers.

Let the first even integer be $x$. Since even integers differ by 2, the next consecutive even integer would be $x + 2$.

The problem states that their sum is 118, so we can write the equation:

$x + (x + 2) = 118$

Now, simplify the equation:

$2x + 2 = 118$

Next, subtract 2 from both sides:

$2x = 116$

Now, divide both sides by 2:

$x = 58$

So, the first even integer is $58$, and the second consecutive even integer is:

$58 + 2 = 60$

Thus, the two consecutive even integers are 58 and 60.

Would you like further explanation or have any additional questions? Here are some related questions you could explore:

1. What would happen if the sum of the integers were a different number, say 130?
2. How would you approach the problem if the integers were consecutive odd numbers instead of even ones?
3. Can you solve a similar problem where the sum of three consecutive integers is given?
4. How can we represent any consecutive integers algebraically?
5. What if the difference between the integers was not 2, but some other even number? How would that affect the solution?

Tip: When solving problems with consecutive integers, it's useful to express the integers in terms of a variable and then use the given conditions to form and solve an equation.