Joe's class will need to reserve 14 seats for the field trip.
First, let's find the total number of students going on the trip after accounting for the two girls who cannot attend:
Total number of students = Number of boys + Number of girls - Number of girls unable to go
Total number of students = 14 boys + 16 girls - 2 girls unable to go
Total number of students = 14 boys + 14 girls
Total number of students = 28 students
Since two students will sit per seat, the number of seats needed can be found by dividing the total number of students by two:
Number of seats needed = Total number of students / Number of students per seat
Number of seats needed = 28 students / 2 students per seat
Number of seats needed = 14 seats
So, Joe's class will need to reserve 14 seats for the field trip.