,
              ==0} ,

e1= D[e Ta^4 + (h Ta),Ta] dTa - D[Tt^4 + h (Tt),Tt] dTt  

e2=da Tt^4 + D[a Tt^4 + h (Tt),Tt] dTt +
             D[-(h Ta) - 2 e Ta^4,Ta] dTa

s1=Solve[e1==0,dTa][[1]]

Solve[(e2//.s1)==0,dTt]

%/.h->0

F2[T0_,h_,e_,a_]:=
Block[{ss},
   ss=FindRoot[
        {T0^4 -   Tt^4 - h (Tt-Ta) +   e Ta^4 ==0,
                a Tt^4 + h (Tt-Ta) - 2 e Ta^4 ==0} ,
        {Ta,300},{Tt,300}];
        Return[ss]]
        

Taa[abs_]:=Ta/.F2[300,10000000,.1,abs][[1]];
Ttt[abs_]:=Tt/.F2[300,10000000,.1,abs][[2]];

Taa[abs_]:=Ta/.F2[300,100,.1,abs][[1]];

Plot[Taa[x],{x,0,3}]

Plot[Taa[x],{x,0,.5}]

Plot[Ttt[x],{x,0,.5},PlotRange->{{0.01,0.5},{300,325}}]