An ‘e’ in the end could alter the meaning. Many a times, these two words are used interchangeably. Garner’s Modern American Usage puts this error at stage 3 which is commonplace even among many well-educated people but is still avoided in careful usage.
Loath Unwilling or reluctant about something
Loathe Strongly dislike someone or something or find it disgusting:
Example
Leader of opposition was loath to speculate on the final outcome of no confidence motion
If voters in general dislike Obamacare, Republican voters positively loathe it