How feasible would it be to get to a planet orbiting directly opposite Earth? Imagine that in addition to Earth, there was a second planet, say of one Earth mass, orbiting the sun - but on the opposite side of the Sun, and at the same orbital radius.

My question is - given today's technology, would it be feasible to try to launch something to reach that planet? A rover, a capsule, or something of the sort is what I have in mind.

There are a couple reasons I initially don't see a solution. First off, the escape velocity of the Earth is about 11.2 km/s. The Earth's orbital velocity around the sun is nearly 30 km/s. This means that if I were to launch a rocket in the opposite direction of Earth's orbit to reach this "second Earth", not only would I have to counter this 30 km/s orbital velocity, but I would have to provide enough thrust for double this velocity in order to maintain a stable orbit around the Sun at the radius that Earth orbits at - but in the opposite direction. I'm not quite sure if rockets can get up to velocities that high - I know that the Juno probe is moving at around 73 km/s, but I believe that was after a series of maneuvers involving a gravitational slingshot.

Perhaps there is another solution? One that popped into my head was to launch it at an angle to the plane of Earth's orbit, but I don't quite know how that would work out, given that unless some serious trajectory corrections were made, the rocket would not arrive anywhere close to the planet - as the planet would have moved in the time the journey took.

Maybe it involves taking a path that is closer to the Sun, and more elliptical? At this point I'm just throwing out everything that comes into my head.

Basically, I'm looking for some sort of general explanation here, with a rough idea that I could build on. And if it isn't possible with today's technology, what do we lack?
Venus has roughly the same gravitational potential as earth and the Venera probes successfully and softly landed there. Similarly, the Apollo space craft landed safely on earth on return. In both cases aerodynamic friction with the atmosphere can be used to get rid of excess velocity in order to enter orbit and eventually land. Thus landing will work cheaper, if there is atmosphere. But at the expense of much more fuel also without (see moon landing again... you'd need stronger descent rockets than Apollo for an exclusively rocket - driven landing) 

Getting there is not a big deal either. Look at the Stereo mission of two satellites which trail earth's orbit more and more to get a better understanding of the sun, gaining more and more separation from earth while (nearly) staying at 1 AU: You get to another position in earth's orbit by just lifting your orbit slightly and waiting for earth to go and the other to catch up (or go slightly towards the sun and be faster yourself).