Let work done by all forces other than conservative forces $={\mathrm{W}}_{\text{others}}$

Work done by conservative forces, ${\mathrm{W}}_{\mathrm{c}\mathrm{o}\mathrm{n}}$ is negative of change in potential energy.

${\mathrm{W}}_{\mathrm{c}\mathrm{o}\mathrm{n}}=-\mathrm{\Delta }\mathrm{U}$

From work energy theorem,

${\mathrm{W}}_{\text{by all forces}}=\mathrm{\Delta }\mathrm{K}$

${\mathrm{W}}_{\text{others}}+{\mathrm{W}}_{\text{con}}=\mathrm{\Delta }\mathrm{K}$

${\mathrm{W}}_{\text{others}}-\mathrm{\Delta }\mathrm{U}=\mathrm{\Delta }\mathrm{K}$

${\mathrm{W}}_{\text{others}}=\mathrm{\Delta }\mathrm{U}+\mathrm{\Delta }\mathrm{K}$

Therefore work done by all forces other than conservative forces is equal to change in total mechanical energy.