Light is made of packets of energy called photons. While photons have no mass, they have momentum. Solar sails capture this momentum with sheets of large, reflective material such as Mylar. As photons bounce off the sail, most of their momentum is transferred, pushing the sail forward.
Source: PLanetry Society FAQ
This statement clearly contradicts the equation of momentum. The FAQ had an explanation for this but I wasn't able to understand it. The page quoted-
$P=mv$ only works for non-relativistic masses. For objects traveling near the speed of light, the universal equation for momentum is $E^2=(pc)^2 + (mc^2)^2$ This allows photons to have momentum, and that momentum can be transferred to another object like a solar sail.
First of all, I wasn't aware of the term "non relativistic mass", I looked for it and got a few articles for "relativistic mass". Though I wasn't convinced how can mass change with velocity but that is a whole another question.
Secondly, I found another paragraph on the same FAQ that states-
In one month of constant sunlight, LightSail's speed would increase by 549 kilometers per hour, roughly the speed of a jet airliner at cruising speed. In 16 months of constant sunlight, LightSail's speed would increase by 8,556 kilometers per hour, fast enough to escape the moon's gravity well.
The speeds mentioned here are far less than speed of light and thus the universal equation of momentum $E^2=(pc)^2 + (mc^2)^2$ should not be valid here.
So my question is "How is the solar sail then able to get momentum from light particicles?"