Example 9 Five numbers $a, b, c, d, e$, their pairwise sums are $183, 186, 187, 190, 191, 192, 193, 194, 196, 200$. If $a<b<c<d<e$, then the value of $a$ is $\qquad$
Analysis: From the problem, we know that $a+b=183, a+c=$ $186, \cdots, d+e=200$. If we can find the value of $a+b+c+$ $d+e$, and note that these ten numbers are the sums of $a$, $b$, $c$, $d$, and $e$ taken two at a time, and that $a$, $b$, $c$, $d$, and $e$ each appear 4 times, then the sum of these ten numbers, 1912, should equal $4(a+b+c+d+e)$, i.e., $a+b+c+d+e$ $=478$. From this, we get $a=(183+186+200)-478$ $=91$.
Explanation: We can also find that $b=92, c=95, d=$ $99, e=101$.