Relativistic energy momentum relation:

From Einstein mass energy relation

E = mc² (1)

Also from variation of mass with velocity relation

m = m₀/(1 – v²/c²)^1/2 (2)

Where m₀ is the rest mass of the object

Put value of m in equation (1) and then square both sides, we get

E²=  m₀²c⁴/(1 – v²/c²)                (3)

As momentum is given by

p = mv

Put equation (2) and square

p² = m₀²v²/(1 – v²/c²)

Multiply both sides by c²

p²c² = m₀²v² c²/(1 – v²/c²)         (4)

Subtract equation (4) from (3) and solve, we get

E² – p²c² = m₀²c⁴

Or E = (p²c² + m₀²c⁴)

This is Relativistic energy momentum relation