tc=ReadList["prubeh.txt",Number];

tc2=Partition[tc,2];

p1=ListPlot[tc2]

{t1e,c1e}={1317,0.006566};

{t2e,c2e}={2.546*^4,0.6758};

taue=t2e-t1e;

cm[t_,t1_,tau_,c1_,c2_]:=c1+UnitStep[t-t1](c2-c1)(1-Exp[-(t-t1)/tau]);

odchylka[t1_,tau_,c1_,c2_]:=Sum[(cm[tc2[[i,1]],t1,tau,c1,c2]-tc2[[i,2]])^2,{i,Length[tc2]}];

nejlepsi=FindMinimum[odchylka[t1,tau,c1,c2],{{t1,t1e},{tau,taue},{c1,c1e},{c2,c2e}}]

p2=Plot[cm[t,t1,tau,c1,c2]/.nejlepsi[[2]],{t,tc2[[1,1]],tc2[[-1,1]]},PlotStyle->Red,PlotRange->All];

Show[p1,p2]

nm=NonlinearModelFit[tc2,cm[t,t1,tau,c1,c2],{{t1,t1e},{tau,taue},{c1,c1e},{c2,c2e}},t]

Show[ListPlot[tc2],Plot[nm[t],{t,tc2[[1,1]],tc2[[-1,1]]},PlotStyle->Red,PlotRange->All],Frame->True]

nm["ParameterConfidenceIntervalTable"]