Question: How to solve ?

I am a beginner in maple.
I encountered a difficulty in solving the below equations:
I have four equations :

192.5 = 6.8889*10^8*(X1/(exp(1199.562077/Y1)-1)+X2/(exp(1199.562077/Y2)-1));
977.9 = 1.755442918*10^7*(X1/(exp(575.7897971/Y1)-1)+X2/(exp(575.7897971/Y2)-1));
4642.7 = 2.20449676*10^5*(X1/(exp(239.9124155/Y1)-1)+X2/(exp(239.9124155/Y2)-1));
6139.8 = 17143.12466*(X1/(exp(143.9474493/Y1)-1)+X2/(exp(143.9474493/Y2)-1));

I would like to calculate X1,X2,Y1,Y2 from the above equations.
Range of X1 is from 0.01..10000
Range of X2 is also from 0.01..10000.
But X1<X2.
Y1 ranging from 5 to 1000 and Y2 ranging from 5..100
 But  Y1>Y2.
I have tried NLPSolve but the objective function gives a large value. At this point how can I solve this? Is there any method with which I can solve the above problem exactly?
Any help is really appreciated;

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