The speed needed to escape from the Earth is 11.2 km/s, and from the Moon 2.38 km/s…

Step 1. The rearranged formula. $T = \dfrac{Mu^2}{3R}$.

Step 2. The Earth. $T = \dfrac{2.016 \times 10^{-3} \times (11\,200)^2}{3 \times 8.314} = 10\,139\ \text{K}$.

Step 3. The Moon. $T = \dfrac{2.016 \times 10^{-3} \times (2380)^2}{3 \times 8.314} = 458\ \text{K}$.

Step 4. The meaning. On the Moon, the rms speed of hydrogen at $390\ \text{K}$ is $\sqrt{\dfrac{390}{458}} = 0.92$ of the escape speed. The molecules are so close to the escape speed that a large fraction of the Maxwell distribution lies above it. Hydrogen leaves in a short time. On Earth, the upper atmosphere at $1000\ \text{K}$ is ten times cooler than $10\,139\ \text{K}$, so the rms speed of hydrogen is only about $0.31$ of the escape speed. But a small fraction of the molecules, those in the far tail of the distribution, move faster than the escape speed. Over millions of years they take most of the hydrogen away. Heavier gases have a much smaller speed and stay.