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I'd like to type the word TRENTo, as the acronym of something. But I'd need the letter "R" to be shifted down a little bit... Something similar to as letter "E" in the \LaTeX symbol. And I'd like to have it outside the math mode if it's possible.

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    \raisebox{-<dimen>}{R}, where <dimen> is a dimension. You may also want to add a small negative kern before the lowered R – Steven B. Segletes Apr 5 at 15:43
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Use \raisebox with a negative argument to lower text, and I suggest some negative kerning, to fill in the gaps. Finally, stick it in a macro for convenience.

\documentclass{article}
\newcommand\TRENTo{T\kern-.4ex\raisebox{-.48ex}{R}\kern-.40ex ENTo}
\begin{document}
\TRENTo{} to the rescue!
\end{document}

enter image description here

If you want to protect it from changing to different font families or shapes due to the underlying text, then you can put it in a group with the desired font properties, as in

\newcommand\TRENTo{\begingroup\normalfont
  T\kern-.4ex\raisebox{-.48ex}{R}\kern-.40ex ENTo\endgroup}
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Look at the \TeX macro definition. TeX has primitive \lower or \raise followed by dimen and box. The box is shifted by the given dimen (in horizontal mode). You tas can be solved by:

\protected\def\TRENTo{T\kern-.4ex\lower.48ex\hbox{R}\kern-.4ex ENTo}

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