Tc1 = 120;
Tw1  =  10;
Tc2 =  20 ;
cpc  =  4680;
cpw  =  4186;
mvC  =  0.111;
mvV  =  1.389;
k = 1750 ;
S = 2;
Δ1 = Tc1  -  Tw1;
Δ2  =  Tc2 - Tw2;

rce1 = 
        Q == 
          k*S*((Δ1 - Δ2)/Log)[Δ(1/Δ)2];
rce2 = Q == mvC *cpc*(Tc1 - Tc2);
rce3 = Q == mvV *cpw*(Tw2 - Tw1);
dos = Solve[{rce2, rce3}][[1]]

Solve[rce1 /. dos]