Do Photons have Mass?

We know that Photon is a packet of energy and anything that has energy will have mass (from energy-mass relation), but nothing that has mass should reach speed of light (from Relativity), obviously Photons do travel with speed of light. How is this possible. All this is a confusing loop of paradox statements, do you know the answer to this question.

Wait there is one more thing, Rest Mass & Relative Mass. 'Rest Mass' is mass measured by an observer with respect to whom the object is at rest and 'Relativistic Mass' is mass of object which is in motion relative to observer (Object will acquire mass due to velocity).

Pic Credits: guardianlv.com & www.quora.com

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