DEFINITION

    Price elasticity of demand is a measurement of the change 
    in the consumption of a product in relation to a change in its price.


Thus in this problem   = 1.8.    (1)


It means, if to follow to the problem LITERALLY, that the dependence Q(consumption) 
of P(price) has the form Q = 1.8*(P-2.50).


But it is clear that it is ILLOGICAL: according to (1), if the price rises over €2.50,
the consumption should increase.


So, actually it should be  Q = -1.8*(P-2.50),
and my first inference that the "problem's composer" is not able to formulate his "economics problem" correctly.


    +-----------------------------------------------------------+
    |      But, thanks to god, I have my common sense           |
    |    in my mind, so I am able to interpret it correctly.    |
    +-----------------------------------------------------------+


Next, I will not consider a profit (since I have no data for calculating it), 
and will consider the REVENUE, only.  The revenue is

    R = P*Q = -1.8*P*(P-2.50),    (2)


and our goal (the goal of the coffee shop, from the context) is to increase the revenue (2).


We write the revenue (2) in equivalent form

    R = -1.8*P^2 + 1.8*2.50*P.


The derivative    is  -2*1.8P + 1.8*2.50,  and at the price P= 2.50€  it is

     = -2*1.8*2.50 + 1.8*2.50 = -4.5.


Since this derivative is negative, then, if the coffee shop wants to increase the revenue, it should decrease the price from €2.50.