As you've noticed there are odd things that can happen using subscripts (and superscripts) in calculations. The solution: Don't use subscript and superscripts in calculations.
But you can have the desired effect (which was posted recently either in this forum or Mathematica.StackExchange - I can't find it at the moment) using the Format statement.
Format[\[Sigma]KEuler, Subscript[\[Sigma], Subscript[K, Euler]]];
\[Sigma]KEuler = 10;
\[Sigma] = 5;
\[Sigma]KEuler/\[Sigma]
(* 2 *)
