I do not have anything to add over the Reusch quote about it being difficult to control, that is, once the carbocation is formed, it is difficult to predict whether a substitution or elimination reaction will take place. If small, large, strongly basic, weakly basic, diffused, polarizable, or any other restriction to the nucleophile applied, I assumed this comment covered those possibilities (unless someone can explain further).
Let me try to explain my point with an example. If you wished to prepare t-butyl chloride from t-butanol, protonation with HCl will result in protonation followed by the rate determining loss of water to form the carbocation. Water can re-attack, an elimination can occur, or chloride can attack. If elimination occurred, HCl can reform the tertiary carbocation. By reforming the carbocation, the competition between elimination can be overcome.
If you wished to convert t-butyl chloride to isobutylene, solvolysis in an organic/water mixture would generate the carbocation. It could be attacked by solvent or water or the elimination reaction would take place. If water attacked, that reaction will be essentially irreversible. If you wished to prepare isobutylene, then change the mechanism so it will be an E2 elimination. No substitution will occur.
Speaking generally, elimination reactions can give a Zaitsev (E1 like) or Hoffmann product. If the question was directed to this possibility, then a good elimination base like KOtBu increase the amount of Hoffmann product that forms. How can that be overcome? Do an E2 elimination is a more polar solvent, like ethanol, to increase the E1 nature of the reaction.
While it is simple to suggest that reactions occur via SN1 or SN2 mechanisms, I prefer to think that they describe the extremes of these reactions. You will find that the leaving group may not completely diffuse away before a nucleophile attacks in an SN1 reaction and some inversion may result. In an SN2 reaction, bond lengthening or breakage may begin before the nucleophile attacks.
In elimination reactions, an additional pair of electrons are involved. The notion of concerted is further stretched and we may even have additional descriptions, such as an E1cb elimination. My comments have been made that recognize these more subtle effects.
Because the rate determining effect of an E1 elimination would be the loss of the leaving group, I do not know how the temperature affects the thermodynamics of a competition v elimination reaction. I simply read that somewhere (probably the Reusch site).