I'm working on the assumption that you mean equal in mass, and by "non-gaseous" you mean composed of elements heavier than hydrogen and helium (technically, Jupiter is mostly liquid or solid due to the extreme pressures). According to our current theories such a body could not evolve naturally, but let's ignore that little fact.
Let's say that the density of the impacting body is 8 times higher than Jupiter, this would make it denser than iron, I don't know if that is realistic at that level of compression by gravity. This would give the impactor a radius half that of Jupiter (If the density is 8 times higher, the volume must by 1/8th, and because volume is proportional to radius cubed, the radius would thus be the cube root of 1/8th, or 1/2).
According to Newton's Impact Depth theory, an impactor will penetrate to approximately its own length times relative density before running out of momentum and this is true regardless of velocity.
Making the simplifying assumption that both bodies have uniform density, the impactor could thus punch 8 times its own diameter into Jupiter, as Jupiter only has twice the diameter of the impactor, it could punch through 4 Jupiters before running out of momentum.
In reality, a disproportionate amount of Jupiter's mass will be in a dense rocky core. If it hits the core then more of its momentum will be absorbed and Jupiter's core will end up being punched out the far side of Jupiter in a great fiery bulge.
So far we haven't considered the energy of the impact. Since the body falls in from outside the solar system, it will be traveling at, at the very least, 70 km/s; this is from a combination of Heliocentric escape velocity at Jupiter's orbit, and Jupiter escape velocity (the two giant masses will pull on each other very strongly and so come together at a great velocity).
The kinetic energy of a Jupiter mass at 70 km/s is 4.65 × 1036 J, while the gravitational binding energy of Jupiter is 2.086 × 1036 J, so the impact could potentially yield a blast powerful enough to overcome the gravitational binding energy of both planets, although only just so - a lot of the mass could coalesce into a new planet.
That amount of energy is equal to the energy released by the sun in 390 years. Jupiter is four times further from Earth than the Sun is, and thanks to the inverse square rule, we only get 1/16th of that, so we receive a blast equal to 24 years of sunlight—all in the matter of hours—now a lot of that energy will be absorbed in the process of blasting Jupiter to pieces but there would be plenty leftover to irradiate Earth (the blast would also be somewhat directional, if the site of impact is aimed towards Earth we are goners as soon as the radiation arrives, but even if the initial radiation doesn't get us, the blast wave of super heated Jupiter atmosphere will)
So the answer to your question, is that Jupiter is blown to pieces and we all die.