We will use $E_L$ for irradiance perpendicular to $l$
Where $l$ is the light vector.
What does this mean? How do I calculate $E_L$?
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The line you quoted says it: $E_L$ is the incoming irradiance at the surface due to the light source under consideration. Less technically, it's a vector representing the intensity and color of the incoming light at that point.
The equation you mention is for a punctual light source (directional, point, or spot light), so in this case $E_L$ would simply be the user-defined RGB color of the light source, multiplied by any relevant attenuation factors—such as shadows, distance attenuation for point/spot lights, and cone angle attenuation for spot lights.