Closest to sensible I can imagine would be wrapping these numbers individually with a function if e is always followed by sign (+or -):
fn[m_. e + e_] := m 10^e;
fn[m_. e] := m;
fn[_] := 0;
fn[1.13903 e - 08]
Handling the case where + is implicit seems awfully convoluted to get right.
I also thought of redefining e as an ...