Maple Eingaben:
T_0 := 273.15;
e_sw := 610.7*exp((17.15*(T-T_0))/(T-38.25));
e_si := 610.64*exp((21.88*(T-T_0))/(T-7.65));
eq := diff(e_sw-e_si,T);
# Bis hier hin kann man die Aufgabe auch von Hand lösen.
solve(eq=0,T);

Maple Output:
> maple
    |\^/|     Maple 7 (SUN SPARC SOLARIS)
._|\|   |/|_. Copyright (c) 2001 by Waterloo Maple Inc.
 \  MAPLE  /  All rights reserved. Maple is a registered trademark of
 <____ ____>  Waterloo Maple Inc.
      |       Type ? for help.
> T_0 := 273.15;
                                                     T_0 := 273.15

> e_sw := 610.7*exp((17.15*(T-T_0))/(T-38.25));
                                                                  T - 273.15
                                          e_sw := 610.7 exp(17.15 ----------)
                                                                  T - 38.25

> e_si := 610.64*exp((21.88*(T-T_0))/(T-7.65));
                                                                  T - 273.15
                                         e_si := 610.64 exp(21.88 ----------)
                                                                   T - 7.65

> eq := diff(e_sw-e_si,T);
            /  17.15            T - 273.15 \           T - 273.15
eq := 610.7 |--------- - 17.15 ------------| exp(17.15 ----------)
            |T - 38.25                    2|           T - 38.25
            \                  (T - 38.25) /

              / 21.88           T - 273.15 \           T - 273.15
     - 610.64 |-------- - 21.88 -----------| exp(21.88 ----------)
              |T - 7.65                   2|            T - 7.65
              \                 (T - 7.65) /

> solve(eq=0,T);
bytes used=1000604, alloc=851812, time=0.71
bytes used=2001480, alloc=1441528, time=1.30
                                                      261.5159344

>