I'm trying to find the percent change in revenue, $I$ from the percent change in profits $P$ and the percent change in costs $E$.
Suppose we are given that $R_1, R_2, E_1$ and $E_2$ are positive.
We have three equations:
$$ \begin{aligned} (1)&\quad P = \frac{(R_2 - E_2) - (R_1 - E_1)}{R_2-E_2}, \quad 0 < P < 1 \\ (2)&\quad C = \frac{E_2 - E_1}{E_2}, \quad 0 < C < 1 \\ (3)&\quad I = \frac{R_2 - R_1}{R_2}, \quad 0 < I < 1 \\ \end{aligned} $$
We know the values of P and C, but not I.
Also assume we know the values of $R_1-E_1 = M_1$ and $R_2-E_2 = M_2$, but we do not know anything about the absolute change in costs or revenue.
Is there a way to find the value of $I$ from the values of $P$ and $C$?
If not, is there a way to approximate the value of $I$?
I think the approximation is complicated, I did the following breakdown:
There are 2 cases, derived from your comment that a lower bound of zero is not acceptable, but first of all let's write $I$ as:
$$I = 1 - \frac{R_1}{R_2}$$
Case 1:
$I$ is arbitrarily close to zero. Yes, it can be, cold shower right at the beginning. For this, we have $R_1 < R_2$ in such a way, that $R_1 \approx R_2 \Rightarrow \frac{R_1}{R_2} \approx 1$. As $R$'s are upper bounds for $E$'s, we have further 2 cases, but we may observe that this bound doesn't matter:
Case 1A:
$E_1 < E_2$ in such a way, that $E_1 \approx E_2 \Rightarrow \frac{E_1}{E_2} \approx 1$. This means that $C$ is arbitrarily close to zero by the same logic for $I$. This relation between $E_1$ and $E_2$ is possible independently of $R_1$ and $R_2$. And implies $M_1 < M_2$ in such a way, that $M_1 \approx M_2$ - arbitrarily close.
Case 1B:
$E_1 << E_2$. This means that $C$ is arbitrarily close to $1$. This relation between $E_1$ and $E_2$ is possible independently of $R_1$ and $R_2$. This implies $M_1 >> M_2$ - arbitrarily far, however this is not possible, as $P > 0 \Rightarrow M_1 < M_2$.
Case summary: having $M_1 < M_2$ and $C$ sufficiently close to $1$ should give a lower bound > 0, otherwise the lower bound is 0.
Case 2:
$I$ is arbitrarily close to $1$. For this, we have $R_1 << R_2$. As $R$'s are upper bounds for $E$'s, we have further 2 cases, but we may observe that this bound doesn't matter:
Case 2A:
$E_1 < E_2$ in such a way, that $E_1 \approx E_2 \Rightarrow \frac{E_1}{E_2} \approx 1$. This means that $C$ is arbitrarily close to zero. This relation between $E_1$ and $E_2$ is possible independently of $R_1$ and $R_2$. And implies $M_1 << M_2$ - arbitrarily far.
Case 2B:
$E_1 << E_2$. This means that $C$ is arbitrarily close to $1$. This relation between $E_1$ and $E_2$ is possible independently of $R_1$ and $R_2$. This implies either $M_1 < M_2$ in such a way, that $M_1 \approx M_2 \Rightarrow \frac{M_1}{M_2} \approx 1$ - arbitrarily close, or $M_1 << M_2$ - arbitrarily far.
Case summary: having $M_1 < M_2$ and $C$ sufficiently close to zero should give an upper bound < 1, otherwise the upper bound is 1.
Total summary: possibly in a contradictory way, $C$ can give both a lower and an upper bound. This is because there is no one bounded $I$, but there are certain cases - so far I covered:
Case 1A: $C \approx 0$ and $P \approx 0 \Rightarrow I \approx 0$
Case 1B: $C \approx 1$ and $P$ any $\Rightarrow I > 0$ - lower bound can be found
Case 2A: $C \approx 0$ and $P \approx 1 \Rightarrow I \approx 1$
Case 2B: $C \approx 1$ and $P$ any $\Rightarrow I < 1$ - upper bound can be found
Cases 1B and 2B tell us, that with the same conditions, we can find bounds - this is how it goes:
$C \approx 1 \Rightarrow E_2 \approx E_1 \Rightarrow P = \frac{(R_2 - E_2) - (R_1 - E_1)}{(R_2 - E_2)} \approx 1 - \frac{(R_1 - E_1)}{(R_2 - E_2)}$ - this should be compared with the formula of $I = 1 - \frac{R_1}{R_2}$:
If $R_2 - E_2 = M_2 \approx R_2 \Rightarrow P > I$, that is, an upper bound.
If $R_1 - E_2 \approx R_1 - E_1 = M_1 \approx R_1 \Rightarrow P < I$, that is, a lower bound.
If both $M_2 \approx R_2$ and $M_1 \approx R_1 \Rightarrow P \approx I$, an approximation.
However, we will never know these, as $R$'s and $E$'s are not given, so I think it is impossible to practically know the bounds. At this point I finish the breakdown, still cases are not covered, e.g. $C \approx 0$ and $P$ any, or $P \approx 1$ and $C$ any, I leave it to you to finish (after correcting any mistakes I made with the above), but I guess practically none of those gave any bounds either.