Let the first even integer be x.
Then, the next consecutive even integer is x + 2.
According to the problem, the sum of the two consecutive even integers is 74.
So, we can write the equation as x + (x + 2) = 74.
By simplifying the equation, we get 2x + 2 = 74.
Subtracting 2 from both sides, we get 2x = 72.
Finally, divide both sides of the equation by 2 to solve for x: x = 36.
Therefore, the two consecutive even integers are 36 and 38. Answer: \boxed{36, 38}.
The sum of two consecutive even integers is 74. What are the two numbers?
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