  Here, we peruse cosmological usage of the most promising candidates of dark
energy in the framework of $f(T)$ gravity theory. We reconstruct the different
$f(T)$ modifed gravity models in the spatially flat FRW universe according to
entropy-corrected versions of the holographic and new agegraphic dark energy
models in power-law and logarithmic corrections, which describe accelerated
expansion history of the universe. We conclude that the equation of state
parameter of the entropy-corrected models can transit from quintessence state
to phantom regime as indicated by recent observations or can lie entirely in
the phantom region. Also, using these models, we investigate the different
erase of the stability with the help of the squared speed of sound.
