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A quick suggestion without a dictionary would be the following:

var('a,b,c,d,e,f,g,h,i,j,k,l,x,y,p,q,r,s,t,u,v,A,B,C,D,E,F,G,H,T,K,L,M,N')
solutions=solve([A - E, A*E - B, B*E - C, C*E - D - 10, D*E + 2], A,B,C,D,E)
justC=[]
for sol in solutions:
    justC.append(sol[2]) #2 is for C
show(justC)