Find two missing numbers

There's an array of 100 numbers. Another array contains only 98 numbers from the first one. Identify two missing numbers.

Constraints:

• Space complexity must be O(1).
  So you can't use any other data structure like a hash-map, etc.
• The arrays are immutable.
  So you can't e.g. sort them.

Math is your friend. For both arrays you need to count a sum of all numbers (sum and sum2), and a sum of squares of the numbers (sq_sum, sq_sum2). Then:

sum - sum2 = a + b
sq_sum - sq_sum2 = a^2 + b^2

(a + b)(a + b) = a^2 + b^2 + 2ab
(a + b)(a + b) - (a^2 + b^2) = 2ab
(sum*sum - sq_sum) = 2ab

(a - b)(a - b) = a^2 + b^2 - 2ab
               = sq_sum - (sum*sum - sq_sum) = 2sq_sum - sum*sum
sqrt(2sq_sum - sum*sum) = sqrt((a - b)(a - b)) = a - b
((a + b) - (a - b)) / 2 = b
(a + b) - b = a

Credit: see link below.

Complexity:

time O(N)

space O(1)

Links:
http://stackoverflow.com/questions/10218791/find-two-missing-numbers