To calculate the force needed to move a brick with a mass of 345 kg a distance of 28 m while doing 1008 J of work, we can use the formula:

$$Force = \dfrac{Work done}{Distance}$$

Substituting the given values, we get:

$$Force = \dfrac{1008 J}{28 m} = 36 N$$

Therefore, a force of 36 N is needed to move the brick while doing 1008 J of work.