Solve Troubles Simultaneous equations – Mathematica Stack Exchange

Code copied below. (I know it is not pretty but still learning.) I am trying to solve a system of two equations for two unkowns. In the upper code I solve one equation for one variable and then substitute into the second equation. This method works and produces a result. (Note I need a numeric solution here not an exact solution.) However, when I try to solve the equations simultaneously Solve returns the result D0->0. Same issue using NSolve. I am not sure what is going on or how to get “fix” Solve to work with both equations simultaneously.

CIn(101):= (*Problem 5.24*)
Clear("Global`*"); Clear(Derivative);
D1(Q_, T_, D0_, k_) = D0*Exp(-Q/(k*T));
EQ1 = D1(Q, 650 + 273.15, D0, 9.62*10^-5) == 5.5*10^-16;
Temp = Solve({EQ1}, {Q});
EQ2 = D1(Q /. Temp((1)), 900 + 273.15, D0, 9.62*10^-5) == 1.3*10^-13;
SolD0 = Solve(EQ2)
EQ3 = D1(Q, 650 + 273.15, D0 /. SolD0((1)), 9.62*10^-5) == 5.5*10^-16;
Solve(EQ3)

Solve({D1(Q, 650 + 273.15, D0, 9.62*10^-5) == 5.5*10^-16, 
  D1(Q, 650 + 273.15, D0, 9.62*10^-5) == 1.3*10^-13}, {D0, Q})
NSolve({D1(Q, 650 + 273.15, D0, 9.62*10^-5) == 5.5*10^-16, 
  D1(Q, 650 + 273.15, D0, 9.62*10^-5) == 1.3*10^-13}, {D0, Q})


During evaluation of In(101):= Solve::ifun: Inverse functions are being used by Solve, so some solutions may not be found; use Reduce for complete solution information.

During evaluation of In(101):= Solve::ifun: Inverse functions are being used by Solve, so some solutions may not be found; use Reduce for complete solution information.

Out(106)= {{D0 -> 0.0000756184}}

During evaluation of In(101):= Solve::ifun: Inverse functions are being used by Solve, so some solutions may not be found; use Reduce for complete solution information.

Out(108)= {{Q -> 2.27762}}

During evaluation of In(101):= Solve::svars: Equations may not give solutions for all "solve" variables.

Out(109)= {{D0 -> 0.}}

During evaluation of In(101):= NSolve::svars: Equations may not give solutions for all "solve" variables.

Out(110)= {{D0 -> 0.}}

I have tried using Reduce but it just returns False.

Any help appreciated.