Your code will only modify the value of $array[7] (which was 8: remember that array indexes start at 0, not at 1). In other words, after $array[7] = $array[7] + $array[8], your array will contain (1, 2, 3, 4, 5, 6, 7, "89", 9, 10).

The index of the element with value 9 is still 8 as it has always been (again, array indexes start at 0, not at 1). No elements have been moved around or deleted. Only the 8th element (the one with index 7) has been altered.