(I)     AB  *   C  =  DE
         *      +      -
(II)     F  *   F  =  AC
        ----------------
(III)   GH  +  AI  =  CH
       (IV)    (V)   (VI)


Solution:
The letters can be reconstructed in a simple way.
(III)  I = 0
(V')   A = 1
(II)   F = 4
(II)   C = 6
(III') G = 5
(IV)   4 | 50+H => H is 2 or 6.
       As C = 6 is used we get H = 2.
(IV)   B = 3
(VI)   E = 8, D = 7


        13  *   6  =  78
         *      +      -
         4  *   4  =  16
       ------------------
        52  +  10  =  62 



References:

Walter Lietzmann;
  Lustiges und Merkw\"urdiges von Zahlen und Formen,
  Verlag Vandenhoeck & Ruprecht,
  G\"ottingen 1955, 8. Auflage, ISBN 3-525-39112-9
  Chap II.5: Vergilbte Manuskripte (p128-131, 21 problems)
  Chap II.13: Anagramme, Kryptogramme, Geheimschriften und dergleichen
  (p191-192, 10 problems)