In Interstellar, we saw Murph, Tom, Prof. Brand are able to send message to Cooper. Then why Cooper or Dr. Brand can't send message as well?
Edit: Original answer was wrong so has been replaced*
Firstly, credit to @Hypnosifl for spotting this on this question.
The communication was two way, but it was very rudimentary going from the wormhole back to Earth. From the screenplay:
Cooper: And if their world didn't show promise?
Doyle: Hence the bravery.
Cooper: Because you don't have resources to visit all twelve.
Doyle: No. Data transmission back through the wormhole is rudimentary, simple binary 'pings' on an annual basis to give some clue as to which worlds have potential...
* If so desired, it can be read in the edit history of this answer
Since I've been talking about Interstellar a lot on these boards I decided to pick up the screenplay on Kindle. There's a line discussing the issue of sending data back through the wormhole in the scene where they first tell Cooper about the wormhole and the Lazarus missions, where Doyle says:
Data transmission back through the wormhole is rudimentary, simple binary 'pings' on an annual basis to give some clue as to which worlds have potential.
So, that seems to suggest there is some special difficulty sending signals back through the wormhole, rather than just a difficulty with sending long-range information, especially since once the Endurance arrives at the other side of the wormhole, they do get detailed info on the planets there from Mann and the other explorers, information which the people at NASA presumably would have liked to have if it were possible:
Doyle: The lost communications came through—
Doyle: The relay on this side cached them.
Doyle flicks through data—
Years of basic data—no real surprises. Miller's site has kept pinging thumbs up, as has Mann ... but Edmunds went down, three years ago.
Later there's a line making clear that once they were on the same side of the wormhole as the Lazarus folks, they could get more detailed info than just the "thumbs up" ping:
Doyle: Look, Dr Mann's data is promising, but we won't get there for months. Edmunds is even further. Miller hasn't sent much, but what she has sent is promising—water, organics...
There's no proof of this, but at a specific point in the film the characters realize that Dr. Brand (senior) solved the gravitational equations long before he sent anyone through. The first explorers knew that they were not only on a one-way trip, but that they wouldn't be sending comprehensive data back. At most a simple ping indicating that they still existed once beyond the wormhole (ie, weren't simply destroyed in the wormhole).
Dr. Brand may have believed that the only hope humanity had was to blindly go through the wormhole, and once on the other side establish communications with the initial explorers and find the best planet.
Thus it's possible that Dr. Brand himself made the equipment so that communications was essentially one way, so as to avoid dissuading further explorers from ceasing the missions. He was, all along, planning on following plan B - the re-seeding of worlds, and had no hope that the humans on Earth would ever be rescued, or that plan A was feasible. This is why he ensured that his child made it onto the mission.
Another possibility, though, is that the wormhole is small, and the earth has more energy than the spaceship. Even if aiming communications at the wormhole from both sides, the ship to earth communications is several magnitudes of order smaller than the energy earth can push through the wormhole from our galaxy. It may merely be an issue of bandwidth and signal to noise ratio.
It isn't one way communication. It's two way.
You're assuming because we see no video logs returned that the communication was only one way - but this wouldn't make any sense.
Firstly, the most probable explanation for Murph's comments at the end of the film about Dr. Brand being all alone is that she received a message from her saying that. This has already been discussed in a previous question.
Secondly, the most probable explanation as to why Cooper never sent a message back is simply - what could he possibly say? He spent a few hours on the surface of the Water Planet and returned to find over twenty years had passed. His children grew up in front of his eyes in minutes on the video log. We can see his emotional out-pour during this powerful, emotional scene. It seems likely that the only reason he didn't get in touch was out of a bewilderment as to what he could possibly say to them. Instead, he chose to finish his mission as quickly as possible, so as to save them.
This answer is actually incorrect, as @Hypnosifl's answer shows. The communiucation was two way, but at a very basic level. This of course means the first point I raised in my answer above becomes rather contentious again.