**Answer:**

Let's assume the two-digit number as 'xy', where x represents the tens digit and y represents the units digit.

The number obtained by the position of its digits can be expressed as 10x + y, where the tens digit is in the tens place and the units digit is in the units place.

According to the given condition, the difference between the two-digit number and the number obtained by the position of its digits is 36. So, we can represent this as:

xy - (10x + y) = 36

Simplifying the above equation, we get:

xy - 10x - y = 36

Combining like terms, we get:

xy - y - 10x = 36

Factoring out y, we get:

y(x - 1) - 10x = 36

Now, let's consider the possible values for x and y:

- If x = 1, then the equation becomes y(1 - 1) - 10(1) = 36, which simplifies to -10 = 36, which is not possible.
- If x = 2, then the equation becomes y(2 - 1) - 10(2) = 36, which simplifies to y - 20 = 36.
- If x = 3, then the equation becomes y(3 - 1) - 10(3) = 36, which simplifies to 2y - 30 = 36.
- If x = 4, then the equation becomes y(4 - 1) - 10(4) = 36, which simplifies to 3y - 40 = 36.
- If x = 5, then the equation becomes y(5 - 1) - 10(5) = 36, which simplifies to 4y - 50 = 36.
- If x = 6, then the equation becomes y(6 - 1) - 10(6) = 36, which simplifies to 5y - 60 = 36.
- If x = 7, then the equation becomes y(7 - 1) - 10(7) = 36, which simplifies to 6y - 70 = 36.
- If x = 8, then the equation becomes y(8 - 1) - 10(8) = 36, which simplifies to 7y - 80 = 36.
- If x = 9, then the equation becomes y(9 - 1) - 10(9) = 36, which simplifies to 8y - 90 = 36.

By solving the above equations, we find that the only possible value for x is 4 and the corresponding value for y is 0.

Therefore, the two-digit number is 40 and the difference between the two digits is 4.

Hence, the correct answer is option A.