日 and 月: Transition from pictographs to hanzi
I'm afraid that an explanation in any book is probably just speculation. The two characters in question have probably been around as long as Chinese characters themselves.

This site (chineseetymology.org) is a very useful resource for tracing the history of Chinese characters. In particular, it appears that both 日 and 月 were sometimes also written without the extra line, as one would expect from a pictogram:

http://www.chineseetymology.org/CharacterImages/Oracle/J10000/j15800/j15869.gif
http://www.chineseetymology.org/CharacterImages/Oracle/J10000/j15800/j15887.gif

with line http://www.chineseetymology.org/CharacterImages/Oracle/J10000/j16400/j16449.gif
without line http://www.chineseetymology.org/CharacterImages/Oracle/J10000/j16400/j16459.gif

although 日 without the line is rare. (Check the entries of 日 and 月 for many more pictures. The history of these characters starts at least some 3000 years ago with the oracle bone script found at the bottom of the page.)

As for interpreting these pictures, 新漢和大辞典 writes the following


  月  
  
  象形。三日月を描いたもので、まるくえぐったように、中が欠けていく月。
  Pictogram. A drawing of a crescent moon, waning as though being hollowed out.
  
  日  
  
  象形。太陽の姿を描いたもの。
  Pictogram. A drawing of the shape of the sun.


In particular, no word about the line in 日.