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The efficiency of a Carnot heat engine in terms of the heat energy that goes into the system and the work done by the system is equal to E = W/H where W is the work done and H is the heat put in. The efficiency can also be given in terms of the temperature of the hot reservoir Th and the temperature of the cold reservoir Tc as E = 1 - Tc/Th.
The Carnot heat engine in the question absorbs 860 J of energy as heat and the work done by the system is 340 J. This gives an efficiency of 340/860. The temperature of the cold reservoir into which heat is rejected is 10 C or 283 K. The temperature of the hot reservoir is given by 340/860 = 1 - 283/Th
=> 283/Th = 1 - 340/860 = 520/860
Th = 283*860/520 = 468 K = 195 C
The temperature of the hot reservoir is 195 C.
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