Is there a scientific way to prove that something is impossible?

I hesitate to call anything impossible because we don’t know what might be capable with tomorrow’s technology. Someone, a few decades back, might think it impossible that I could be posing this question to people all over the world right now, for instance.

It is said that we can’t scientifically disprove the existance of something. Can we also not prove the impossibility of something?

For a more tangible example, today in lecture my professor said that “it is impossible, not just difficult but impossible, to isolate y in this equation” regarding e^(xy) + sqrt(x + y) – 4 = 0. I couldn’t help but wonder if he has proof for that statement or if it’s just not possible with present methods.