Thank you for all the response.
Using Matlab to solve, I think this is what the code would be:
[R1,R2,R3,R4]=solve('R1=269.0(R2+R3+R4)/(R2+R3+R4-269.0)','R2=267.8(R1+R3+R4)/(R1+R3+R4-267.8)','R3=268.8(R1+R2+R4)/(R1+R2+R4-268.8)','R4=267.3(R1+R2+R3)/(R1+R2+R3-267.3)','R1','R2','R3','R4')...