Some chemical reactions while producing the product molecules releases heat to the surroundings and such reactions are called “exothermic reactions”. Is it true that such systems must be showing energy loss in the process meaning “ΔE ” must be negative?
No. If means that to maintain the temperature of the products equal to the temperature of the reactants, you need to remove heat, and, form the first law, if you do this, then $\Delta E$ is negative. However, if you don't remove the heat, the temperature of the products will be higher than those of the reactants, and $\Delta E$ of the system will then be zero (as required by the first law).