The Solow model and his 1956 paper Reading through Robert Solow's 1956 paper, entitled "The Theory of Economic Growth", I was hoping to find his fundamental difference equation. I was wondering if the following equation is indeed that very equation, $$\dot{r}=s(r)F(r,1)-nr.$$
In my textbook, the fundamental difference equation is given by $$\dot{K}=f(K,L)-\delta K. \tag1$$
I am having a bit of trouble reading through Solow's paper (am a novice at economics), and was wondering if someone can locate the equation that is similar to $(1)$.
I will assume that you are talking about the Solow, R. M. (1956). A contribution to the theory of economic growth. The quarterly journal of economics, 70(1), 65-94. as to my best knowledge Solow did not published paper entitled the "Theory of Economic Growth" in 1956 and the first equation you use in your question is from the paper.  

Moreover, I also think that you either made a mistake or your textbook assumed whole output is saved (which would be most unorthodox) because normally the equation (1) should be looking like this:

$$\dot{K} = s F(K,L) - \delta K$$

See for example the Romer's Advanced Macroeconomics or Blanchard's et al Macroeconomics an European Perspective (both authors use slightly different notation but the point is both textbooks show that change in capital depends on the fraction of saved output not the whole output). 

In the 1956 paper the closest equivalent of equation (1) in your question would be equation (3) in Solow's paper:

$$ \dot{K} = sF(K,L)$$

The reason why the depreciation is not explicitly there as a separate term is that Solow assumes that "Output is to be understood as net output after making good the depreciation of capital".