That is probably the classiest way I've seen yet to do the second problem. Since I gave Python code above, here it is for your version:

    >>> from random import shuffle
    >>> def test(n, missing, extra):
    ...     t = [i if i != missing else extra for i in range(1, n + 1)]
    ...     shuffle(t)
    ...     return t
    ...
    >>> def solve(list):
    ...     diff, diffsq, n = 0, 0, 1
    ...     for i in list:
    ...         diff += i - n
    ...         diffsq += i*i - n*n
    ...         n += 1
    ...     sum = diffsq / diff
    ...     return {'extra': (sum + diff)/2, 'missing': (sum - diff)/2}
    ...
    >>> solve(test(7633507, missing=3518688, extra=4057456))
    {'missing': 3518688L, 'extra': 4057456L}