How are PPP, nominal exchange rates and inflation related? This Forbes article discusses how changes in the market exchange rate can be used to estimate an inflation rate thanks to the principle of purchasing power parity (PPP).

Can someone distill this process a little better? I can follow the steps mentioned in the article, but the underlying principles are still not clear to me.
Let $P$ denote the price in the home country, $E$ represent units
of domestic currency used to buy one unit of foreign currency, and
$P^{*}$ represent the price level in the foreign country. Now, PPP
implies that:
$$
P=EP^{*}
$$
 In other words, prices when expressed in the same currency are equalized
across countries. Log-differentiate and take changes and obtain:
$$
\hat{P}=\hat{E}+\hat{P}^{*}
$$
 where hats denote changes. Rearrange, and find that:
$$
\hat{E}=\hat{P}-\hat{P}^{*}
$$
In other words, the changes in exchange rate inform one of relative changes
in price levels (inflation). This is what is know as relative PPP