Learn Dutch: Aan de ene kant investeren wij, aan de andere kant is er verlies. - On the one hand we invest, on the other hand there is a loss.

In Dutch, the conjugated verb must be the second element in a main clause (the V2 rule). Because both clauses start with a phrase setting up the contrast (Aan de ene kant and aan de andere kant), the verb must come immediately after. This pushes the subjects (wij and er) right behind their verbs.

Since this lesson is about words like daarentegen and echter, could I use them here?

You could, but you would replace the second half of the phrase to avoid being redundant. The phrase aan de ene kant ... aan de andere kant is a fixed pair that already shows strong contrast. If you wanted to use daarentegen (on the other hand), you might rephrase the whole sentence to something like: Wij investeren, er is daarentegen verlies.

Why is er used in is er verlies?

Here, er acts just like the English word "there" in "there is" or "there are". Because verlies (loss) is an undefined subject (it doesn't say "the loss" or "my loss"), Dutch uses the dummy subject er to introduce it. Combined with the verb zijn (to be), er is means "there is".

Why do ene and andere both get an -e at the end?