When the question is asking about favorability, it is really asking about the magnitude of the Gibb's free energy. The more negative this value, the more favorable a reaction is. Gibb's depends on enthalpy and a temperature scaled entropy: (G=H-T*S). When we think of nucleophilic elimination, we know that a Hydrogen atom is removed by a nucleophilic group resulting in our final product. Since a Hydrogen is removed in elimination, while left intact during substitution, there are more final species formed during an elimination reaction. According to general chemistry principles, this means that there was a larger increase in entropy compared to the substitution. As temperature increases this larger entropy becomes more noticeable as it is now scaled by a larger T. Therefore at low temperature, the enthalpy term dominates Gibbs and the substitution reaction prevails. However as T grows, so does the entropy term and at high T this overrides enthalpy, making the elimination reaction more favorable.

When the question is asking about favorability, it is really asking about the magnitude of the Gibbs free energy. The more negative this value, the more favorable a reaction is. Gibbs depends on enthalpy and a temperature scaled entropy: $$\Delta G=\Delta H-T\Delta S$$

When we think of nucleophilic elimination, we know that a hydrogen atom is removed by a nucleophilic group resulting in our final product. Since a hydrogen is removed in elimination, while left intact during substitution, there are more final species formed during an elimination reaction. According to general chemistry principles, this means that there was a larger increase in entropy compared to the substitution. As temperature increases this larger entropy becomes more noticeable as it is now scaled by a larger $T$. 

Therefore at low temperature, the enthalpy term dominates Gibbs and the substitution reaction prevails. However as $T$ grows, so does the entropy term and at high $T$ this overrides enthalpy, making the elimination reaction more favorable.