Elasticity of demand is almost always assumed to be negative. It is assumed that there is an inverse relationship between price and quantity demanded. If you want to buy 2 hamburgers for
$5 each you aren't suddenly going to want to buy 3 hamburgers if they now cost
$10 each. If this isn't the case it means that consumers aren't rational which blows up 99% of the models economics has to offer.
Because the elasticity of demand is always negative it can be assumed that if I say X is the elasticity of demand I mean X is negative because elasticity of demand is always negative. If I say -X is the elasticity of demand you can still assume that it is negative because a) I said it explicitly, and b) it is always true.
At this point it's just a matter of preference and doesn't matter either way, I just wanted to explain why it really doesn't matter since someone who understands what elasticity of demand means will understand that it will always be negative in almost all scenarios.
Personally, I think that explicitly saying that the elasticity of demand is negative is a better choice since I can imagine some fringe scenarios where a product being expensive leads to that product being sold more often, (I think of caviar as an example for these types of products, where consumers buy it precisely because its expensive) but for most economic models the assumption holds.