2. Let real numbers $a, b, c, d, e$ satisfy $a<b<c<d<e$, and among the 10 sums of any two numbers, the smallest three sums are $32, 36, 37$, and the largest two sums are $48, 51$. Then
$$
e=
$$
$\qquad$
2.27.5.

From the problem, we know
$$
\begin{array}{l}
a+b=32, a+c=36, \\
c+e=48, d+e=51 .
\end{array}
$$

It is easy to see that, $c-b=4, d-c=3, d-b=7$.
Thus, $a+d=(a+b)+(d-b)=39$.
Therefore, $b+c=37$.
Then $2 a=(a+b)+(a+c)-(b+c)=31$.
So $a=15.5, b=16.5, c=20.5$,
$$
d=23.5, e=27.5 \text {. }
$$

Upon verification, the above values satisfy the conditions. Hence, $e=27.5$.