Is it possible to partition $\{1, 2, 3, \ldots, 28\}$ into two sets $A$ and $B$ such that both of the following conditions hold simultaneously: (i) the number of odd integers in $A$ is equal to the number of odd integers in $B$; (ii) the difference between the sum of squares of the integers in $A$ and the sum of squares of the integers in $B$ is $16$?