If you were in a plane, then the point that is r meters away at a bearing of a degrees east of north is displaced by r * cos(a) in the north direction and r * sin(a) in the east direction. (These statements more or less define the sine and cosine.)
Although you are not in a plane--you're working on the surface of a curved ellipsoid that models the Earth's surface--any distance less than a few hundred kilometers covers such a small part of the surface that for most practical purposes it can be considered flat. The only remaining complication is that one degree of longitude does not cover the same distance as a degree of latitude. In a spherical Earth model, one degree of longitude is only cos(latitude) as long as a degree of latitude. (In an ellipsoidal model, this is still an excellent approximation, good to about 2.5 significant figures.)
Finally, one degree of latitude is approximately 10^7 / 90 = 111,111 meters. We now have all the information needed to convert meters to degrees:
The northwards displacement is r * cos(a) / 111111 degrees;
The eastwards displacement is r * sin(a) / cos(latitude) / 111111 degrees.
For example, at a latitude of -0.31399 degrees and a bearing of a = 30 degrees east of north, we can compute
cos(a) = cos(30 degrees) = cos(pi/6 radians) = Sqrt(3)/2 = 0.866025.
sin(a) = sin(30 degrees) = sin(pi/6 radians) = 1/2 = 0.5.
cos(latitude) = cos(-0.31399 degrees) = cos(-0.00548016 radian) = 0.999984984.
r = 100 meters.
east displacement = 100 * 0.5 / 0.999984984 / 111111 = 0.000450007 degree.
north displacement = 100 * 0.866025 / 111111 = 0.000779423 degree.
Whence, starting at (-78.4437, -0.31399), the new location is at (-78.4437 + 0.00045, -0.31399 + 0.0007794) = (-78.4432, -0.313211).
A more accurate answer, in the modern ITRF00 reference system, is (-78.4433, -0.313207): this is 0.43 meters away from the approximate answer, indicating the approximation errs by 0.43% in this case. To achieve higher accuracy you must use either ellipsoidal distance formulas (which are far more complicated) or a high-fidelity conformal projection with zero divergence (so that the bearing is correct).