Solving Laplacian in $\mathbb{R}^2$

Question

We have our partial differential operator in $\mathbb{R}^2$, $L=-\Delta$, and want to find a fundamental solution. So we equal it to Dirac's delta, and then we Fourier Transform it, obtaining the equation $|\xi|^2\mathcal{F}[E]=1$, where E is the fundamental solution. So, we observe that the principal value of $\displaystyle\frac1{\xi^2}$ is the fourier transform of our fundamental solution. By taking the inverse fourier transform, we get that $\displaystyle E=\frac1{2\pi}\log\frac1{|x|}$. Can someone explain the calculations involved here?