Let $S=[s_1,s_2,$dots,$s_n]$ be a sequence of characters. Let $x$ be the sequence derived from $S$ in which the elements are first shuffled, then two random elements $s_i$ and $s_j$ are removed. Design an efficient algorithm that takes as input the two sequences $S$ and $x$ and determines the two missing elements of $S$ in $x.$ The only data structure allowed to solve this exercise are arrays.

For example, let's take the two sequences:

$S=[e,x,a,m,p,l,e]$

$x=[x,e,e,m,l]$

The algorithm must find that the elements $\text{'}a\text{'}$ and $\text{'}p\text{'}$ are missing in $x.$

Analyse the time complexity of the designed algorithm and prove its efficiency.