Setting up a radiation heat transfer problem

I am trying to solve a radiation heat transfer problem. The problem is set up like this: Two spherical shells of radius R whose surfaces are separated by a distance R. One shell, call it A, has a steady heat flux of Q and the other, call it B, does not. Both also radiate to ambient (‘surface’ C) at 0 C.

To solve this I use these equations:

$$ dot{q}_i = frac{varepsilon_i A_i (E_{b,i}-J_i)}{1-varepsilon_i} quad text{for } i = 1.. N $$
$$ dot{q}_i = A_i sum_{j=1}^N F_{i,j}(J_i-Jj) quad text{for } i = 1.. N $$

So for sphere A, the left hand side of both equations is Q and for the others it is zero. The view factors are as follows:

FAB = 0.0294

FAC = 1-FAB

FBA = FAB

FBC = FAC

FCA = FAC*SurfaceAreaA/SurfaceAreaC

FCB = FBCC*SurfaceAreaA/SurfaceAreaC

FBC = FAC

Since the temperature of C is set, I have 6 equations in 5 unknowns (TA, TB, JA, JB, JC). When I try to solve this in matlab using the nonlinear equation solver I cannot get a solution. Did I make a mistake in setting this up?

Below is the matlab code I am using for equations 1 and 2.

function F = TWO_SPHERES_AMBIENT(J)
% Function called by FSOLVE

sig = 5.670374419e-8;    % S-B constant [W/m^2*K^4]
r = 0.1;                 % Radius of Balls A and B [m]
R = 10;                  % Radius of "Ambient" sphere
g = 50000;               % Equiv. Internal Generation of Ball A [W/m^3]
vol = 4*pi*(r^3)/3;      % [m^3]
sa = 4*pi*(r^2);         % Surface Area of Balls A and B [m^2]
SA = 4*pi*(R^2);         % Surface Area of "Ambient" Sphere [m^2]
totgen = g*vol;          % Total Heat Generated in Ball A [W]
flux2surf = totgen/sa;   % Total Flux to the Surface of Ball A [W/m^2]
eps1 = 0.7;              % Generating ball emis.
eps2 = 0.5;              % Nongenerating ball emis.
eps3 = 0.99;             % "Ambient" emis. (1, Except Div. By Zero Below)
FAB = 0.0294;            % View Factors
FAC = 1 - FAB;
FBA = FAB;
FBC = FAC;
FCA = FAC*sa/SA;
FCB = FBC*sa/SA;
FCC = 1 - FCA - FCB;     % Plays no role in equations below. (J(3)-J(3)=0)
FBC = FAC;
% BELOW IS IS THE RETURN TO FSOLVE. J IS WHAT FSOLVE PASSES IN, F IS
% RETURNED BACK.
% J(1) IS BALL A RADIOSITY 
% J(2) IS BALL B RADIOSITY
% J(3) IS 'AMBIENT' RADIOSITY
% J(4) IS BALL A TEMPERATURE
% J(5) IS BALL A TEMPERATURE
% J(6) IS "Ambient" TEMPERATURE
% EQUATIONS 1, SET TO ZERO AS REQUIRED BY FSOLVE.
F(1) = sa*(FAB*(J(1) - J(2)) + FAC*(J(1) - J(3))) - totgen;
F(2) = sa*(FBA*(J(2) - J(1)) + FBC*(J(2) - J(3)));
F(3) = SA*(FCA*(J(3) - J(1)) + FCB*(J(3) - J(2)));
% EQUATIONs 2, SET TO ZERO AS REQUIRED BY FSOLVE 
F(4) = eps1*sa*(sig*J(4).^4 - J(1))/(1-eps1) - totgen;
F(5) = eps2*sa*(sig*J(5).^4 - J(2))/(1-eps2);
F(6) = eps3*SA*(sig*273.15.^4 - J(3))/(1-eps3);