A literal answer to your question is the [math-style=upright] package option of unicode-math, which you can switch on and off with the commands
\unimathsetup{math-style=upright}
\unimathsetup{math-style=ISO}
For example:
\documentclass[varwidth=10cm, preview]{standalone}
\usepackage{physics}
\usepackage[math-style=upright]{unicode-math}
\begin{document}
\begin{align*}
TDD &= \frac{18}{9} = 2' \\
TF &= TI-TDD = 25-2 = 23' \\
TR &= \frac{18-5}{9} = 2' \\
TT &= TI+TRT+TD+TRS = 25+2+5+1 = 33'
\end{align*}
\end{document}

That said, I wouldn’t recommend you use this technique. (Although I do recommend that you use unicode-math if you’re allowed to!) The \mathrm solution is still supported and will work fine.
I personally find it handy to declare something like \newcommand\TDD{\ensuremath{\mathop{\mathrm{TDD}}}} and then write \TDD in the equations. If you might for some reason want to write x \TDD or \TDD \TI instead of x \cdot \TDD and \TDD \cdot \TI, the \mathop makes x TDD TI behave like log log x (that is, typeset like an operator name).
\documentclass[varwidth=10cm, preview]{standalone}
\usepackage[T1]{fontenc}
\usepackage{physics}
\newcommand\upvar[1]{\ensuremath{\mathop{\mathrm{#1}}}}
\newcommand\TD{\upvar{TD}}
\newcommand\TDD{\upvar{TDD}}
\newcommand\TF{\upvar{TF}}
\newcommand\TI{\upvar{TI}}
\newcommand\TR{\upvar{TR}}
\newcommand\TRS{\upvar{TRS}}
\newcommand\TRT{\upvar{TRT}}
\newcommand\TT{\upvar{TT}}
\begin{document}
\begin{align*}
\TDD &= \frac{18}{9} = 2' \\
\TF &= \TI-\TDD = 25-2 = 23' \\
\TR &= \frac{18-5}{9} = 2' \\
\TT &= \TI+\TRT+\TD+\TRS = 25+2+5+1 = 33'
\end{align*}
\end{document}
This is just like typing \log or \sin. An existing shorthand for this is \operatorname{TDD} from amsmath.
\mathrm{TDD}although it is possible to change the default (probably an answer on site already I'll look... – David Carlisle Feb 08 '19 at 14:11\mathrm{TR}and\mathrm{TDD}(not\text) but you could do this, replacing\mathttby\mathrmhttps://tex.stackexchange.com/a/63000/1090 – David Carlisle Feb 08 '19 at 14:15&sign, another one after it). Look here https://i.imgur.com/hqF3sLJ.png – sound wave Feb 08 '19 at 14:23\mathrmjust to be around each identifier not spanning&) If you get an error such as! Missing } inserted.do not even look at the pdf output, it is just a possible debugging aid, tex makes no attempt at making sensible typeset output after an error. – David Carlisle Feb 08 '19 at 14:28mathttwithmathrm... it works! I just get this error:Improper \halign inside
$$'s.l.22 \end{align*}
Displays can use special alignments (like \eqalignno) only if nothing but the alignment itself is between
– sound wave Feb 08 '19 at 14:40$$'s. So I've deleted the formulas that preceded this alignment.alignshould never be in math mode so I don't see how you could get that error or have formulas before the alignment? The code in my answer generates no error. – David Carlisle Feb 08 '19 at 14:41