Can Escherichia coli survive on glucose and water alone?
The minimum requirement for E. coli and other bacteria to grow and survive is called minimal medium.  It's even defined at Merriam-Webster:


  a medium that contains only inorganic salts, a simple carbon source (as carbon dioxide or glucose), and water


Water and glucose are pretty easy, but the source of salts may often change; regardless, you really need some potassium, phosphate, and nitrogen for amino acid synthesis.  This page has a bunch of information on bacterial growth, including some "recipes" for a few bacterial strains.  For E. coli, the classic media is M9, which over at Sigma is made of:


  
  33.9g Na₂HPO₄.7H₂O
  15g KH₂PO₄
  5g NH₄Cl
  2.5g NaCl
  
  
  per litre of solution. 


Here are some other recipes.