Consider the reactions
(i) (CH3)2CH−CH2BrC2H5OH−−−−−→(CH3)2CH−CH2OC2H5+HBr
(ii) (CH3)2CH−CH2BrC2HSO−−−−−−→(CH3)2 CH CH2OC2H5+Br−
The mechanism of reactions (i) & (ii) are respectively
SN2 and SN2
Since rearrangement do not occur in the given nucleophilic substitution reactions, therefore carbocations are not the intermediate in these reactions. Thus both the reactions occur by SN2 mechanism