Final answer:
To find the two-digit number, we can write two equations using the given information and solve them simultaneously. The two-digit number is 20.
Step-by-step explanation:
To solve this problem, let's call the tens digit of the unknown two-digit number 'x' and the ones digit 'y'. We know that the sum of the digits is 2, so we can write the equation x + y = 2. We also know that reversing the digits decreases the number by 18, so we can write the equation (10y + x) - (10x + y) = 18.
Simplifying the second equation, we get 9y - 9x = 18. Dividing both sides of the equation by 9, we have y - x = 2. We can now solve these two equations simultaneously to find the values of x and y.
Substituting y = 2 + x into the first equation, we have x + (2 + x) = 2. Combining like terms, we get 2x + 2 = 2. Subtracting 2 from both sides, we have 2x = 0. Dividing by 2, we get x = 0. Substituting this value back into y = 2 + x, we have y = 2. Therefore, the two-digit number is 20.