Two Non-Linear Equations, Two unknowns

So, I think this is that easy. Two non-linear equations, two unknowns. I know I once knew how to do this, but now I don't seem to be able to do it. I tried the min command, but that's just for arrays. I tried fsolve(E1,E2) which didn't work because it wants "double". Fminbnd didn't work either, I think because it can't handle two functions. I know my answer should be around Ts=290 and Ta=250, ish. It's just a simple command somewhere, but I can't find it. Any help would be appreciated. Thanks for taking the time!

   alphaS=0.11;    ta=0.53;    alphaA=0.3; tprimea=0.06;   alphaprimea=0.31;
  C=2.5;  
  So=6.28e7;  %Solar Constant, p.110
  sigma=5.67e-8;  %Boltzman's Constant, p. 110
  %syms Ta Ts

E1=@(Ts,Ta)ta*(1-alphaS)*So/4-C*(Ts-Ta)-sigma*Ts^4*(1-alphaprimea)+...
    sigma*Ta^4;
E2=@(Ts,Ta)(1-alphaA-ta*(1-alphaS))*So/4+C*(Ts-Ta)+sigma*Ts^4*...
    (1-tprima-alphaprimea)-2*sigma*Ta^4;

Answer 1

[Star Strider]

One problem is a typo in ‘E2’, where there’s an ‘e’ wanting in ‘tprima’. With that and creating ‘E1E2’ from both functions:

alphaS=0.11;    ta=0.53;    alphaA=0.3; tprimea=0.06;   alphaprimea=0.31;
C=2.5;
So=6.28e7;  %Solar Constant, p.110
sigma=5.67e-8;  %Boltzman's Constant, p. 110

E1=@(Ts,Ta)ta*(1-alphaS)*So/4-C*(Ts-Ta)-sigma*Ts^4*(1-alphaprimea)+...
    sigma*Ta^4;
E2=@(Ts,Ta)(1-alphaA-ta*(1-alphaS))*So/4+C*(Ts-Ta)+sigma*Ts^4*...
    (1-tprimea-alphaprimea)-2*sigma*Ta^4;

E1E2 = @(B) [E1(B(1),B(2));  E2(B(1),B(2))];
B0 = [290; 250];
TsTa = fsolve(E1E2, B0)

TsTa =
     4.5604e+003
     3.5995e+003

Since this may not be the result you want, you may need to experiment with it, particularly with respect to a different ‘B0’. (This code assumes both equations equate to zero, as fsolve requires.)

[Daniel]

Yeah, forgot to mention they were equal to zero, thanks. And a typo, dang it all. I could have spent all night and never found that. Not working quite yet, but a definte step in the right direction, thanks!

[Star Strider]

My pleasure!

[Daniel]

Got it. FIxed it by fixing another typo I had in my code while waiting for some help. Thanks again, I really appreciate it.

[Star Strider]

Again, my pleasure.

Glad you got it sorted.