To solve this question, the user needs to know that an odd number can only be obtained by adding an odd number of odd numbers. Therefore, the sum of two integers whose product is odd must be an even number.

Now, let's go through each option and explain why it is right or wrong:

A. Odd number: This option is incorrect because the sum of two integers whose product is odd cannot be odd. Adding two odd numbers together results in an even number.

B. Even number: This option is correct. The sum of two integers whose product is odd must be an even number. This is because the product of two odd numbers is odd, and odd + odd = even.

C. Prime number: This option is incorrect because the sum of two integers whose product is odd has nothing to do with prime numbers. Prime numbers are numbers that are only divisible by 1 and themselves.

D. Divisible by difference of two numbers: This option is incorrect because there is no relation between the sum of two integers whose product is odd and the difference of the two numbers.

E. Perfect square: This option is incorrect because there is no relation between the sum of two integers whose product is odd and perfect squares.

Therefore, the answer is:

The Answer is: B. Even number