Let the rate of the stream be x km/h.

The boat's rate when the river speeds up the boat by 
adding its speed of x km/h to the boat's speed giving
10+x km/h.

The boat's rate when the river slows the boat down and
subtracts its speed of x km/h from the boat's speed 
giving 10-x km/h.

Time = Distance/Rate

Downstream time = (Downstream Distance)/rate = 26/(10+x)

Upstream time = (Upstream Distance)/rate = 14/(10-x)

Those times are equal.

26/(10+x) = 14/(10-x)

Might as well divide both sides by 2

13/(10+x) = 7/(10-x)

Cross-multiply:

13(10-x) = 7(10+x)

130-13x = 70+7x
   -20x = -60
      x = 3 km/h

That's the answer.  The rate of the river is 3 km/h.  The story
is that he went down the river at 13 km/h for 26 km. for the 
first 2 hours and came back at a slower 7 km/hr and only made 
it 14 km of the way back when the second 2 hours was up.  

Edwin