(I)     AB  *   C  = DEB
         +      +      -
(II)    AC  *   B  = FBB
        ----------------
(III)   GE  -  FE  =  CE
       (IV)    (V)   (VI)


Solution:
The letters can be reconstructed in a simple way.
(III.1)  E = 0
(V.2)    F = 1
(VI.3)   D = 2
(II)     B != 0
(II)     B*C = B (mod 5)
      =>   C = 1 (mod 5)  with B != 0
      =>   C = 6  as F is already 1.
(V)      B = 4
(III.2)  G = 7
(IV.2)   A = 3


        34  *   6  = 204
         +      +      -
        36  *   4  = 144
       ------------------
        70  -  10  =  60 



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)