for (i = 0; i < 10; i++)
cin >> array[i];
you are overwriting your array at position 0 here. Initialize i to 1.
Someone else might write the function for you. I will not. You need to deliver a little bit more. How are you going to step through the array to check the sum of two numbers and hit all the possible solutions (logically you should be able to figure that out... the coding we can help you with)?
