EDTA is there to protect your DNA from divalent metal-dependent nucleases.

Salt has some influence on annealing, but it does not play critical role.

Thank you Misha Soskine  

If you need to measure duplex melting temperatures (i.e. for modified oligos), EDTA is added to remove divalent cations like Ca2+ and Mg2+ that strongly affect melting points by stabilizing duplex.

In this case, concentration of monovalent cations like Na+ is also important - the more salt you have in your solution, the more duplex is stabilized, and the higher melting point is observed. So this buffer is needed to ensure standard conditions for the annealing.