As far as quick & easy formulae go, the only two examples I know of relate to two points either on the same parallel or the same meridian.
Same parallel: "Departure":
dist = (change in longitude in degrees) x cosine (average latitude) x 60
Same longitude:
dist = change in latitude in degrees x 60.
A formula that works for E/W and N/S will use spherical trigonometry, and will appear to be immensely complex!
It has been covered a few times before on these forums. Try the search feature, going back two years.
cheers,
O8