Finding the temperature of Earth from temperature of Mars and its distance from Sun I am to compute the temperature of planet--in fact I've already found out it's Earth--knowing only: 


the surface temperature of Mars (210 K) and its distance from Sun (1.524 AU)
and of course distance of Earth from Sun (1 AU). 


I have no data concerning the temperature of Sun, surfaces of the planet, etc. What formula should I use? Thank you.
I might as well write up my comment into an answer.

One of my new favorite tools in my equations toolkit is the formula for effective temperature:
$$T=\left( \frac{L(1-a)}{16 \pi \sigma D^2} \right)^{\frac{1}{4}}$$
where $T$ is the temperature of the planet, $L$ is the star's luminosity, $a$ is the planet's albedo, $\sigma$ is the Stefan-Boltzmann constant, and $D$ is the distance between the star and the planet. To find the star's luminosity, simply solve for $L$:
$$L=\frac{T^4 16 \pi \sigma D^2}{1-a}$$
where all the terms are for the first planet (Mars). Now, knowing $D$ for Earth, solve for $T$ on Earth.

All you have to know for this that isn't in the question is albedo. That could be tricky, because it's not given. You could assume that it's the same for both planets - and so solve not for $L$ but for $L(1-a)$ - but that might not be better than an approximation.